Question

Whitney reflects MNO across the line x = 1 to form M'N'O' on the coordinate plane above. List the congruent side and angle pairs for MNO and M'N'O.

M = (2,-8)
N = (3,-4)
O = (9,-6)

Answer 1

The line x = 1 is like the y-axis, it's completely vertical but it goes through the point (1, 0) on the x-axis. To make up for this difference, we can add 2 to the x-values we find if we reflected these points about the y-axis.

Reflecting points about the y-axis multiplies the x-values by -1. So:

(2, -8) = (-2, -8)
(3, -4) = (-3, -4)
(9, -6) = (-9, -6)

Now add 2 to the x-values:

(-2, -8) = (0, -8) = M'
(-3, -4) = (-1, -4) = N'
(9, -6) = (-7, -6) = O'

Corresponding sides and angles for MNO will relate to M'N'O'.

So:

Angle M = Angle M'
Angle N = Angle N'
Angle O = Angle O'

Side MN = Side M'N'
Side NO = Side N'O'
Side OM = Side O'M'