Question

What is the equation for the line of reflection for ABCD to A’B’C’D’? Explain.

Answer 1

`y = (4)/(5) x - (1)/(5)`

Explanation:

calculate midpoint of AA'

calculate midpoint of DD'

A(-5,1)

A'(-1,-3)

D(1,5)

D'(3,1)

then midpoint is

`(x_(d) + x_(d^(1)))/(2) = 2 \\ (y_(d) + y_(d^(1)))/(2) =3 \\ \\ (x_(a) + x_(a^(1)))/(2) = - 3 \\ (y_(a) + y_(a^(1)))/(2) = - 1`

then find slope

`( y_(2) -y_(1))/(x_(2) -x_(1)) = (4)/(5)`

then apply equation

`y = (4)/(5) x + b`

substitute any point of the 2 midpoints to find b

`b = ( - 1)/(5)`

then the equation is

`y = (4)/(5) x - (1)/(5) \\`