Q:

Explain how you would find the coordinates of the imageof (5.2) if it was reflected over the x-axis and then thatimage was reflected over the y-axis. What would be theend result?

Accepted Solution

A:
The result of reflecting point (5.2) over the x-axis and then reflecting that image over the y-axis is (-5, -2)Explanation:In this exercise, we need to make two transformations to find the image of the point (5, 2):First: Reflect the point over the x-axis.Second: Next, reflect that image over the y-axis.Let's call the (5, 2) point A, so the first transformation is as follows:1. Reflect the point over the x-axis.For any point (x, y), if you reflect this point over the x-axis you should multiply the y-coordinate by -1, so you get:[tex](x,y)\rightarrow(x,-y)[/tex]In this case, we have [tex]A(5,2)[/tex], so the image is:[tex]A'(5,-2)[/tex] 2. Next, reflect that image over the y-axis.For any point (x, y), if you reflect this point over the x-axis you should multiply the x-coordinate by -1, so you get:[tex](x,y)\rightarrow(-x,y)[/tex]In this case, we have [tex]A'(5,-2)[/tex], so the image is:[tex]A''(-5,-2)[/tex] The result of reflecting point (5.2 )over the x-axis and then reflecting that image over the y-axis is (-5, -2)Learn more:Transformations: