Looking again at A$^\prime$ and A$^$ its midpoint lies at the origin (0,0), and the same is true for all other points. The same calculations work for the other points: in each case, the $x$-coordinate does not change and the $y$-coordinate changes sign.īelow is a picture of the original points, their reflections over the $x$-axis and then the reflections of the new points over the $y$-axis: If we were to fold the plane along the $x$-axis, the points A and A$^\prime$ match up with one another. Reflecting over the $x$-axis does not change the $x$-coordinate but changes the sign of the $y$-coordinate. Similarly the coordinates of $B$ are $(-4,-4)$ while $C = (4,-2)$ and $D = (2,1)$.īelow is a picture of the reflection of each of the four points over the $x$-axis: The coordinates of $A$ are $(-5,3)$ since $A$ is five units to the left of intersection of the axes and  3 units up. In order to help identify patterns in how the coordinates of the points change, the teacher may suggest for students to make a table of the points and their images after reflecting first over the $x$-axis and then over the $y$-axis: Point Thus the knowledge gained in this task will help students when they study transformations in the 8th grade and high school. Based on the definition of reflection across the y-axis, the graph of y1(x) should look like the graph of f (x), reflected across the y-axis.
![reflection over y axis reflection over y axis](https://i.ytimg.com/vi/8uh2_jQ-rMk/maxresdefault.jpg)
As students answer a question correctly, a portion of the mystery picture will be revealed. Students will reflect points over the x-axis, y-axis, y x and y -x. Later students will learn that this combination of reflections represents a 180 degree rotation about the origin. In this self-checking digital mystery picture activity, students will practice reflecting a point over a given line.
![reflection over y axis reflection over y axis](https://www.geogebra.org/resource/kdsb5whm/XqDkTsHmegAxDbqZ/material-kdsb5whm-thumb@l.png)
This means that if we reflect over the $x$-axis and then the $y$-axis then both coordinates will change signs.