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 An object and its reflection have the same shape and size, but the figures face in opposite directions. If the pre-image is labeled as ABC, then the image is labeled using a prime symbol, such as A'B'C'. The original object is called the pre-image, and the reflection is called the image. Thus the knowledge gained in this task will help students when they study transformations in the 8th grade and high school. A reflection can be done across the y-axis by folding or flipping an object over the y axis. Later students will learn that this combination of reflections represents a 180 degree rotation about the origin. This means that if we reflect over the $x$-axis and then the $y$-axis then both coordinates will change signs. Next, note that any point (x, y) of the co-ordinate plane, when reflected in the line y x, it becomes (y, x). So this point will be an invariant point when reflected in the line y x. Clearly these two lines intersect at the point O (0, 0). Similarly when we reflect a point $(p,q)$ over the $y$-axis the $y$-coordinate stays the same but the $x$-coordinate changes signs so the image is $(-p,q)$. Probably you want the equation of the image of the line y 2x in the line y x.When we reflect a point $(p,q)$ over the $x$-axis, the $x$-coordinate remains the same and the $y$- coordinate changes signs so the image is $(p,-q)$.The teacher may wish to prompt students to identify patterns in parts (b) and (c):
The goal of this task is to give students practice plotting points and their reflections.
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