Question

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

Answer 1

Answer:

$y = \frac{4}{5} x - \frac{1}{5}$

Step-by-step explanation:

calculate midpoint of AA'

calculate midpoint of DD'

A(-5,1)

A'(-1,-3)

D(1,5)

D'(3,1)

then midpoint is

$\frac{x_{d} + x_{d^{1}}}{2} = 2 \\ \frac{y_{d} + y_{d^{1}}}{2} =3 \\ \\ \frac{x_{a} + x_{a^{1}}}{2} = - 3 \\ \frac{y_{a} + y_{a^{1}}}{2} = - 1$

then find slope

$\frac{ y_{2} -y_{1}}{x_{2} -x_{1}} = \frac{4}{5}$

then apply equation

$y = \frac{4}{5} x + b$

substitute any point of the 2 midpoints to find b

$b = \frac{ - 1}{5}$

then the equation is

$y = \frac{4}{5} x - \frac{1}{5}$