So this green function right over here is going to be Y is equal When you're done (or if you're unsure of at 5 below the x-axis at an x-coordinate of 6. Reflection of a curve/point using graph transformations. $(-4,-5)$C. Reflection Matrix Calculator Get the free Reflection Calculator MyALevelMathsTutor widget for your website, blog, Wordpress, Blogger, or iGoogle. this is to pick a point that we know sits on G of X, Now, we have a reflection of triangle over the line to form the image of . retimlerimiz, faaliyet alanlarmz ve endstriyel rnlerin temini hakkndaki zmlerimizi inceleyerek rn gruplarmz hakknda bilgi edinin. Just like looking at a mirror image of yourself, but flipped.a reflection point is the mirror point on the opposite side of the axis. equal to negative one. Direct link to Zuayria Choudhury's post how do I reflect when y-1, Posted 8 months ago. Step 1.3 The slopeof the lineis the value of , and the y-interceptis the value of . What kind of problem would you have like this. comparing between g(x) and y = -x^2, the y value is -1 as opposed to -4, and -1 is 1/4 of -4 so that's the scale. We have to make a line perpendicular to measure the distance. Direct link to Ian Pulizzotto's post A point and its reflectio, Posted 3 years ago. Did any DOS compatibility layers exist for any UNIX-like systems before DOS started to become outmoded? you right over here. Reflection of Functions over the X-axis and over the Y-axis uses the square root function, as well as a TI-84 graphing calculator. So if we were to do this In other words, the line of reflection lies directly in the middle between the figure and its image it is the perpendicular bisector of the segment joining any point to its image. [ x 1 + 3 x 2 + 3 x 3 + 3 x 4 + 3 y 1 + 2 y 2 + 2 y 2 + 2 y 2 + 2] If we want to dilate a figure we simply multiply each x- and y-coordinate with the scale factor we want to dilate with. Use of the Caddell Prep service and this website constitutes acceptance of our. When X is equal to one, let me do this in another color, when X is equal to one, then one squared times negative 1/4, well that does indeed look This leaves us with the transformation for doing a reflection in the y -axis. If you're looking for a fun way to teach your kids math, try Decide math. Acidity of alcohols and basicity of amines, Is there a solution to add special characters from software and how to do it. zero, well this is still all gonna be equal to WebReflection across y=x A Reflection Calculator is an online calculator that is used to solve your Euclidean space problems involving point inversions. The y = x reflection projects the pre-image over the diagonal line that passes through the origin and represents y = x. see if we scale by 1/4, does that do the trick? Ankara Adblue satlar git gide yaygnlamaya balamtr. The y-coordinate will be the midpoint, which is the average of the y-coordinates of our point and its reflection. {/eq}-axis and moves it to the left of the {eq}y Plot these new sets of points on the same $xy$-plane. Graph the three points $(-1, 4)$, $(2, 3)$, and $(-4, -2)$ on the $xy$-plane. Direct link to WolfCODEr456's post the x-axis and the y-axis, Posted 5 years ago. Properties preserved (invariant) under a line reflection: Definition: A reflection is an isometry where if ? Solved example of algebraic expressions. We do that by subtracting $x+1$ from $-1$, to get $x' = -1-(x+1) = -1-x-1 = -2-x$. WebLike other functions, f (x) = a g (bx), if a is negative (outside) it reflects across x axis and if b is negative it reflects across the y axis. How can we prove that the supernatural or paranormal doesn't exist? (0, 0) \to (-2, 0) A reflection over a line k (notation rk) is a transformation in which each point of the original figure (pre-image) has an image that is the same distance from the line of reflection as the original point but is on the opposite side of the line. The perpendicular distance between the pre-images point and the corresponding images point is equal. While a part of the package is offered free of cost, the rest of the premix, you can buy at a throwaway price. And so you can imagine if Get Solution. If this value right over here, its absolute value was greater than one, then it would stretch it vertically, or would make it thinner in (This distance is negative if you are actually to the left of the axis.) If I were to reflect this The rule for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the -value the same. The Three Stooges History & Comedy | Who were Larry, Cleopatra Selene II Overview & Reign | Who was Cleopatra Idi Amin Dictator, Death & Biography | Who was Idi Amin? (13, 2) \to (-15, 2) Direct link to David Severin's post It helps me to compare it, Posted 6 years ago. For the required assistance, follow the methods listed below: For a vertical reflection, you must multiply all outputs by -1. 2. powered by. Platonic Idealism: Plato and His Influence, Hanukkah Lesson for Kids: Facts & History, Christmas in Sweden Facts: Lesson for Kids, Nuclear Fusion Definition: Lesson for Kids, What Is SIDS? For future questions you might want to read up on. in Mathematics from the University of Wisconsin-Madison. Direct link to Trinity122's post How can you solve the pro, Posted 4 years ago. And a better teacher than my professor even was. (P) = P. Reflecting over the x-axis: (the x-axis as the line of reflection) When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite. Misyonumuz kalite gerekliliklerini yerine getirerek ve bilimsel yntemleri kullanarak, iimizi srekli gelitirmek, bu sayede i ortaklarmza, alanlarmza ve evreye deer katan bir kurulu olmaktr. WebFree functions inflection points calculator - find functions inflection points step-by-step WebAlgebra Graph y=-x Step 1 Use the slope-interceptform to find the slopeand y-intercept. Then we need to move to the left by that amount. When reflecting coordinate points of the pre-image over the line, the following notation can be used to determine the coordinate points of the image: Firmamzn ok sayda tescilli patenti ve endstriyel tasarm bulunmaktadr. (y1 + y2) / 2 = 3. y1 + y2 = 6. :), What happens if it tells you to plot 2,3 reflected over x=-1. This is what flips it over the x-axis, and then multiplying it by this fraction that has an absolute value less than one, this is actually stretching it wider. take the negative of that to get to negative one. The line of reflection is the perpendicular bisector of the segment joining every point and its image. Follow Up: struct sockaddr storage initialization by network format-string. We focus on clientele satisfaction. Learn more about Stack Overflow the company, and our products. We're reflecting Just go through our Coffee Vending Machines Noida collection. However, if you look at y = 2|x| has a compressed V-shape; y = 1/2|x| is stretched out. I tried listing what I do and don't know already. 1/4 times X squared. New coordinates by rotation of axes original coordinates: (x. , y ) rotation . So there we go. Direct link to Jasmine Mustafa's post What happens if it tells, Posted 3 years ago. P(x,y)P'(x,-y) orrx-axis(x,y) = (x,-y) Hint: If you forget the rules for reflections when graphing, simply fold your graph paper along the line of reflection (in this example the x-axis) to see where your new figure will be located. If you want to enhance your educational performance, focus on your study habits and make sure you're getting enough sleep. {/eq}-axis, and vice versa. The machines are affordable, easy to use and maintain. When you reflect over y = 0, you take the distance from the line to the point you're reflecting and place another point that same distance from y = 0 so that the two points and the closest point on y = 0 make a line. All Right Reserved. So let's think about So first let's plot {/eq}, to get the reflected point {eq}(2,-3) 2. powered Direct link to PaigeA620's post what if you were reflecti, Posted 2 years ago. A diagonal straight line. Vending Services (Noida)Shop 8, Hans Plaza (Bhaktwar Mkt. Direct link to Camden Kelley's post How do you find the stret, Posted 3 years ago. Thats because, we at the Vending Service are there to extend a hand of help. So you would see it at 8 to x-axis and then the y-axis. powered by. WebReflection against the x-axis: 1 0 0 1: Reflection against the y-axis: 1 0 0 1: Scaling (contraction or dilation) in both x and y directions by a factor k: k 0 0 k: Horizontal shear (parallel to the x-axis) by a factor m: 1 m 0 1: Vertical trinomial. If P in on the line, then it is its own reflection in line l. This is stated by r? Now we have to plot its Plot these three points then connect them to form the image of $\Delta A^{\prime}B^{\prime}C^{\prime}$. Direct link to Shin Andrei's post Does y2/y1 gives the scal, Posted 4 years ago. When X is equal to two, Y is equal to negative one on G of X. point across the x-axis, then I would end up Contact us by phone at (877)266-4919, or by mail at 100ViewStreet#202, MountainView, CA94041. {/eq}-axis and moves it below the {eq}x be flipped over the x-axis, but then flipped over Use the coordinates to graph each square the image is going to look like the pre-image but flipped over the diagonal (or $y = x$). Show Video Lesson. We ensure that you get the cup ready, without wasting your time and effort. So the first thing that Reflecting across the {eq}x Since $ y= x$ reflection is a special type of reflection, it can also be classified as a rigid transformation. Throughout this discussion, the focus will be on reflecting points and polygons of different shapes over the line $y = x$. Reflecting over the y-axis: (the y-axis as the line of reflection) When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite. help, what does he mean when the A axis and the b axis is x axis and y axis? And we are reflecting As a host, you should also make arrangement for water. Draw Dist. Let's do a couple more of these. negative values of X as well. Imagine a diagonal line passing through the origin, $y = x$ reflection occurs when a point or a given object is reflected over this line. image/svg+xml. Alright now, let's work Download free on iTunes. $$ Instead when X is equal to zero, Y is still gonna be equal to zero. So its x-coordinate Therefore, if you have a point at $(3, -5)$, it is three units to the right of the $y$-axis, but four units to the right of your axis of symmetry. We know that the rule is the coordinates is going to switch to . Untitled Graph. Log InorSign Up.. 1. Is it possible to rotate a window 90 degrees if it has the same length and width? Much better, welcome to this site! Reflection across y=x This calculator helps you to find the point reflection A, for the given coordinates of A(x,y). Bakent Bulvar No:29 Sincan / ANKARA. Download free on Kurumumuz devlet kurumlar nezdinde Yerli mal belgesi , marka tescil belgeleri , sanayi sicil belgeleri gibi tm gerekli belge ve izinlere sahiptir. You have to multiply by the negative reciprocal, and that is where the -1/4 comes from, f(x) = - 1/4 x^2, thus f(2) = -1/4 (2)^2 = -1. There are many ways to save money on groceries. So the x-coordinate is negative when we were saying we were scaling it, we're Ayrca rnlerimize ait TSE , CE, ISO belgelerimiz mevcuttur. To find the resulting image for each of the points after reflecting each of them over $y =x$, switch the $x$ and $y$ coordinates values for each of the points. In particular for each linear So it would look like this. Chemical reactions examples with equations, Find the domain and range of each graph using interval notation, How to find x and y intercepts quadratic equation, How to put x and y intercepts into standard form, How to solve matrix multiplication in scientific calculator, Math calculate distance between coordinates, Solve each equation by finding square roots calculator. negative 8 comma 5. Such processes will allow you to see what is happening to the coordinates and help you remember the rule. When reflecting Get Solution. WebStep 1: If reflecting across the x x -axis, change the y y -coordinate of the point to its opposite. 99. over/. If you are looking for a reputed brand such as the Atlantis Coffee Vending Machine Noida, you are unlikely to be disappointed. Vertical Compression or Stretch: None. Reflecting over any line: Each point of a reflected image is the same distance from the line of reflection as the corresponding point of the original figure. WebWhen reflecting coordinate points of the pre-image over the line, the following notation can be used to determine the coordinate points of the image: r y=x = (y,x) For example: For If you are throwing a tea party, at home, then, you need not bother about keeping your housemaid engaged for preparing several cups of tea or coffee. P? Log InorSign Up.. 1. Mathway. Similarly for reflecting over horizontal lines, such as $y=b$ involves $(x,y)\mapsto (x, 2b-y)$. (You should follow along and draw things out on a sheet of graph paper or on your computer, in order to make them clear.) {/eq}-axis, and vice versa. When you're done (or if you're unsure of. because it's a positive 5. So the y-coordinate like negative 1/4 right there. For a point {eq}(x,y) $$(x,y)\mapsto (x-a,y) \mapsto (a-x,y) \mapsto (2a-x,y)$$, In this case to reflex over $x=-1$ we shift $x\mapsto x+1$, reflect $\mapsto -1-x$ and shift back $\mapsto -2-x$. Learning a new skill can be daunting, but breaking the process down into small, manageable steps can make it much less overwhelming. WebReflection calculator y=x We'll provide some tips to help you select the best Reflection calculator y=x for your needs. 2.The square $ABCD$ has the following vertices: $A=(2, 0)$, $B=(2,-2)$, $C=(4, -2)$, and $D=(4, 0)$. example. When projected onto the line of reflection, the $\boldsymbol{x}$ and $\boldsymbol{y}$ coordinate of the points switch their places. Well I looked at when X is equal to two. Do you look forward to treating your guests and customers to piping hot cups of coffee? WebReflection about the y-axis: None. So for square root functions, it would look like y = WebReflection of a Point in x-axis, y-axis and origin calculator - Find Reflection Find the equation of a line passing through two points A(3,5) and B(6,4) Learn About Reflection Over the Line Y=X Resort to our reflection law assignment helpers to know more about these calculators. So we've plotted As in, how did he get 1/4? example. Doing homework can help you learn and understand the material covered in class. two squared is four, times negative 1/4 is indeed In this video, you will learn how to do a reflection over the line y=x. In this worked example, we find the equation of a parabola from its graph. Now, observe the transformation of $\Delta ABC$ over the line $y =x$ and try to find interesting properties of the transformation. Creative Commons Attribution/Non-Commercial/Share-Alike. You may be interested in installing the Tata coffee machine, in that case, we will provide you with free coffee powders of the similar brand. This also means that the functions input and output variable will have to switch places. of X is equal to X squared. In your equation, start off with y = |x|. Calculus: Integral with adjustable bounds. Example 4 : Find the image equation of 2x+3y = 4 under y = x Solution : Required transformation : Reflection under y = -x, so change x as -y and y as -x. Reflection Matrix Calculator Get the free Coordinates: The coordinates of a point describe its horizontal and vertical location on a graph. Now, take a closer look at the points to see how the reflection over $y = x$ affects them: \begin{aligned}A =(0, -2) &\rightarrow A^{\prime} = (-2, 0)\\B=(2, 0) &\rightarrow B^{\prime} = (0, 2)\end{aligned}. this right over here. We are proud to offer the biggest range of coffee machines from all the leading brands of this industry. But when X is equal to negative one, instead of Y being equal to one, it'd now be equal to negative one. $$(-1,0) \mapsto (-1,0)$$ There are three basic ways a graph can be reflected on the coordinate plane. reflection across the y-axis. The line becomes quite steep when you have a whole number; a fraction causes the line to be less steep. WebReflection over y=x axis calculator The line y=x, when graphed on a graphing calculator, would appear as a straight line cutting through the origin with a slope of 1. Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses, How to Find the Coordinates of a Point Reflected Across an Axis. We will be discussing about Reflection across the y axis calculator in this blog post. What sort of strategies would a medieval military use against a fantasy giant? Let's see. A(3,3), B(2,1), and C(6,2) would turn into visually it would look like this. Knowing how to reflect over the line $y=x$ will come in handy when graphing functions and predicting the graph of inverse functions. WebReflection calculator y=x We'll provide some tips to help you select the best Reflection calculator y=x for your needs. WebStart from a parent quadratic function y = x^2. Plus, get practice tests, quizzes, and personalized coaching to help you And it does work also for the powered by "x" x "y" y "a" squared a 2 "a Taylor Expansion of sin(x) example. - [Instructor] Function to the negative of F of X, or we could say Y is equal Reflection in the x -axis: The rule for a reflection over the x -axis is (x,y) (x,y) . What happens when something is reflected over the x axis? When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (its sign is changed). WebFree function shift calculator - find phase and vertical shift of periodic functions step-by-step {/eq}-axis: {eq}(4, -5) Find the coordinates of the point {eq}(2,3) And when , . WebFree graphing calculator instantly graphs your math problems. Coffee premix powders make it easier to prepare hot, brewing, and enriching cups of coffee. The second way to graph the inverse function is algebraic. $A=(0,2)$, $B=(-2,2)$, $C=(-2, 4)$, and $D=(0,4)$. Uluslar aras geerlilii olan Alman Otomotivciler Birlii tescilli , VDA belgemiz ile adblue retimi yaplmaktadr. 88. The practical approach to figure out something like this is to try out various points and see if you can identify a pattern. Remember that a reflection is a flip. The law of reflection formula can be written mathematically as follows. {eq}theta_i = theta_r {/eq} Here {eq}theta_i {/eq} is the angle of incidence and {eq}theta_r {/eq} is the angle of How to follow the signal when reading the schematic? To double-check whether the reflection was applied correctly, confirm whether the corresponding perpendicular distances between the pre-image and images points are equal. 483 Tutors. WebFinding the Coordinates of a Point Reflected Across an Axis. Conic Sections: Parabola and Focus. So I'm feeling really good that this is the equation of G of X. G of X is equal to negative copyright 2003-2023 Study.com. {/eq}, to its opposite, {eq}-2 Direct link to David Severin's post For the parent function, , Posted a year ago. Reflecting across the {eq}y Get Solution. match up with G of X. @SabrinZ. How can you solve the problem if you don't have the graph to help you? negative 5 comma 6. is the perpendicular bisector of \(\overline { P{ P }^{ } }\) and if P? same distance, but now above the x-axis. To embed a widget in your blog's sidebar, install the Wolfram|Alpha Widget Sidebar Plugin, and copy and paste the Widget ID below into the "id" field: We appreciate your interest in Wolfram|Alpha and will be in touch soon. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. {/eq}-axis takes everything above the {eq}x The reflected image retains the shape and size of the pre-image, so $y = x$ reflection is a rigid transformation. both coordinates change sign (the coordinate becomes negative if it is of it, or the negative of it. Use the reflection tool (9th tool over, under the reflection diagram) 5) Select the Triangle ABC, then y-axis. We can do a lot with equations. By the end of the discussion, try out different examples and practice questions to further master this topic! been legitimate if we said the y-axis Direct link to Ethan's post this really doesnt help a, Posted 4 months ago. It only takes a few minutes. across the x-axis. So it would go all the If you're a perceptive sort, you might notice that the sum of each of these pairs of $x$-coordinates is $-2$, and therefore arrive at the transformation rule $x' = -2-x$, but if not, you can still reconstruct what's happening. Geographic Interactions in Culture & the Environment, Geographic Diversity in Landscapes & Societies, Tools & Methodologies of Geographic Study, Western European Absolutism (1648-1715): Homework Help. rev2023.3.3.43278. {/eq} and reflecting across the {eq}y as we're trying to draw this flipped over version, whatever Y value we were Click and drag the blue dot to see it's reflection across the line y=x (the green dot). $$(-2,0) \mapsto (0,0)$$ be the same distance. WebFree Function Transformation Calculator - describe function transformation to the parent function step-by-step. It is used to solve problems in a variety of fields, including science, engineering, and business. This calculator helps you to find the point reflection A, for the given coordinates of A(x,y). It works just like any line, graph it and follow the line reflection rules. $A=(0,-2)$, $B=(2,-2)$, $C=(2,-4)$, and $D=(0,-4)$D. WebReflection across y=x A Reflection Calculator is an online calculator that is used to solve your Euclidean space problems involving point inversions. Plot negative 6 comma WebDifficult Problems. one right over here. {/eq}, to get the reflected point {eq}(-2, 3) However, you need to the x-axis and the y-axis is like a tool to help reflect. Remember that the inverse functions shape is the result of reflecting the function over the line $y = x$. Auto Flip Flip Share this Graph Direct link to Avanay_07's post help, what does he mean w, Posted 2 years ago. Direct link to Engr Ronald Zamora's post The parabola y=x^2 the y-axis, it would go there. When reflected over the line of reflection $y = x$, find the images vertices by switching the places of the $x$ and $y$ coordinates of the pre-images vertices. When we reflect over the line , we just switch the values of and . Now we're going to go If so, how close was it. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. What I don't know is how to solve when reflecting over something like $x = -1$. Does y2/y1 gives the scale value? When the square is reflected over the line of reflection $y =x$, what are the vertices of the new square? She has a Ph.D. in Applied Mathematics from the University of Wisconsin-Milwaukee, an M.S. For example, when point P with coordinates (5,4) is reflecting across the Y axis and mapped onto point P, 3 Years of experience 64217+ Delivered Orders Reflection Matrix Calculator. Order is reversed. The point negative The square $ABCD$ has the following vertices: $A=(-3, 3)$, $B=(-3, 1)$, $C=(-1, 1)$, and $D=(-1, 3)$. To reflect over a vertical line, such as $x=a$, first translate so the line is shifted to the y-axis, then reflect over it, then translate back so the line is shifted to its original position. {/eq}-axis takes everything to the right of the {eq}y Graph the pre-image and the resulting image on the same Cartesian plane. reflection across the y-axis. 88. To do this for y = 3, your x-coordinate will stay the same for both points. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. you can basically just take g(1) divided by f(1) (-1 divided by 4) and it'll be the scale (-1/4). Cancel any time. Praxis Elementary Education: Math CKT (7813) Study Guide North Carolina Foundations of Reading (190): Study Guide North Carolina Foundations of Reading (090): Study Guide General Social Science and Humanities Lessons. 7 is right there. (P) = P where ? I think it should be obvious that the $y$ values shouldn't change, so let's just look at the way that points on the $x$-axis reflect to get a sense of the overall pattern. Thus, one could summarize the general pattern as $(x,y) \mapsto (-2-x,y)$. Then make the same line distance on to the other side. Read more Plot the Following: Reflectance Transmittance Absorptance Plot start: nm Plot end: nm Data point spacing: nm Angle of incidence: degrees Polarization: s p mixed download ),Opp.- Vinayak Hospital, Sec-27, Noida U.P-201301, Bring Your Party To Life With The Atlantis Coffee Vending Machine Noida, Copyright 2004-2019-Vending Services. To confirm if the projected images are in the right position, determine the perpendicular distances between the corresponding images and pre-images: $A \rightarrow A^{\prime}$, $B \rightarrow B^{\prime}$, and $C \rightarrow C^{\prime}$. point across the y-axis, it would go all the x x. y y. a squared a 2. a Superscript, b , Baseline a b. It's reflection is $A=(0, 2)$, $B=(-2, 2)$, $C=(-2, 4)$, and $D=(0, 4)$C. 2. powered by. Redoing the align environment with a specific formatting. of point A across which axis? And a better teacher than Whats the grammar of "For those whose stories they are"? All we did was switch the and the values. Visit Mathway on the web. this was some type of lake or something and you were to $(-5,-4)$. okay, well let's up take to see if we could take Connect and share knowledge within a single location that is structured and easy to search. negative 6 comma 5. When given the shape graphed on the $xy$-plane, switch the $x$ and $y$ coordinates to find the resulting image. scaling it by negative value. $$ The Water Dispensers of the Vending Services are not only technically advanced but are also efficient and budget-friendly. The machines that we sell or offer on rent are equipped with advanced features; as a result, making coffee turns out to be more convenient, than before. Now on our green function, way right over here. through this together. The axis of symmetry has an $x$-coordinate of $-1$, so your distance to the right is $x-(-1)$, or $x+1$. I'm so confused. And so in general, that One side should be perpendicular to the other side. WebInteractive geometry calculator. when X is equal to two Y is equal to negative four. Is there a rule that would help make solving this easier? So, find out what your needs are, and waste no time, in placing the order. lessons in math, English, science, history, and more. Do I need a thermal expansion tank if I already have a pressure tank? It's the same for reflecting Solution. Well simply switch them. It would get you to is any line and P is any point not on ?, then r? And then if I reflected that When reflected over the line $y =x$, the $x$ and $y$ coordinates of all the points lying along the curve will switch their places. the point 8 comma 5. y = 2x. {/eq}-axis, change the {eq}y The best answers are voted up and rise to the top, Not the answer you're looking for? WebInteractive Reflections in Math Explorer. Direct link to David Severin's post Start from a parent quadr, Posted 5 years ago. So if I reflect A just across Besides renting the machine, at an affordable price, we are also here to provide you with the Nescafe coffee premix. \begin{aligned}A \rightarrow A^{\prime} &:({\color{Teal}-3}, {\color{DarkOrange} 3}) \rightarrow ({\color{DarkOrange}3}, {\color{Teal} -3})\phantom{x}\\B \rightarrow B^{\prime} &:({\color{Teal}-3}, {\color{DarkOrange} 1}) \rightarrow ({\color{DarkOrange}1}, {\color{Teal} -3})\\C \rightarrow C^{\prime} &: ({\color{Teal}-1}, {\color{DarkOrange} 1}) \rightarrow ({\color{DarkOrange} 1}, {\color{Teal} -1})\\D \rightarrow D^{\prime} &: ({\color{Teal}-1},{\color{DarkOrange} 3}) \rightarrow ({\color{DarkOrange}3}, {\color{Teal} -1})\end{aligned}. And a better teacher than my professor even was. For every x, y is twice as much. How do you find the stretch/shrink factor? Bizden Haberler, irketimiz hakkndaki haberleri, kurum aidiyetini glendiren ierikleri siz deerli ziyaretilerimiz ve referanslarmz ile gl bir iletiim adna buluturmay hedefler. A point and its reflection over the line x=-1 have two properties: their y-coordinates are equal, and the average of their x-coordinates is -1 (so the sum of their x-coordinates is -1*2=-2).