Question

Give the coordinates of the points after a reflection over the line y=-4

A( 4,5) A' (_,_)

B(0,4) B' (_,_)

C(-2,1) C' (_,_)


use algebraic representation and please show your work !

Answer 1

The line y = -4 will be the midpoint between the y-value of X and the y-value of X'. That means
.. (y +y')/2 = -4
.. y +y' = -8
.. y' = -8 -y
The x-coordinate remains unchanged.

A' = (4, -8-5) = (4, -13)

B' = (0, -8-4) = (0, -12)

C' = (-2, -8-1) = (-2, -9)