90.5k views
5 votes
Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces Y′(9, 3)

1 Answer

4 votes
To determine the line of reflection that produces Y′(9, 3), we need to find the midpoint between Y and Y′, which we can call M. We can then find the slope of the line that passes through Y and M, and then find the perpendicular line that passes through M. This perpendicular line is the line of reflection.

First, let's find the coordinates of M:

M = ((-9 + 9)/2, (3 + 3)/2)
M = (-9/2, 3)

The slope of the line passing through Y and M is:

m = (3 - 3)/(-9 - (-9/2))
m = 0

Since the slope is 0, the line passing through Y and M is a horizontal line. The equation of this line is:

y - 3 = 0

Now we need to find the perpendicular line that passes through M. Since the slope of the line passing through Y and M is 0, the slope of the perpendicular line is undefined. This perpendicular line is a vertical line passing through M. The equation of this line is:

x - (-9/2) = 0

Simplifying this equation, we get:

x + 9/2 = 0

Therefore, the line of reflection that produces Y′(9, 3) is the vertical line x + 9/2 = 0.
User MrCartoonology
by
8.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories