Rectangle abcd is reflected over the x-axis. what rule shows the input and output of the reflection, and what is the new coordinate of a'?
a. (x, y) -> (y, -x) a' is at (1, 5)
b. (x, y) -> (-y, x) a' is at (-1, -5)
c. (x, y) -> (-x, y) a' is at (5, 1)
d. (x, y) -> (x, -y) a' is at (-5, -1)

Option D; (x, y) -> (x, -y); A' is at (-5, -1)

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Step-by-step explanation:

Reflection is one of the linear transformations which reflect any object along the line of reflection. The size of the shape remains the same but the orientation changes.

Reflection along the x-axis means that the sign of y-coordinate changes but the sign of the x-coordinate remains same.

From figure we identified the coordinates of point A:

A (-5,1)

So, A' will be (x,-y)

=> A' = (x,-y) = (-5,-1)

So, Option D (x, y) -> (x, -y); A' is at (-5, -1) is correct.

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap