Question

suppose line m is the line with the equation x = - 5, line n is the line with the equation y = 1, line g is the line with the equation y = x, and line h is the line with the equation y=-2. given a(9, - 3), b(6, - 4) and c(-1, - 5), what are the coordinates of the vertices of △abc for the reflection r_g? a□ (type an ordered - pair)

Explanation:

Step1: Reflect point C(-1, - 5) over y = x

When reflecting a point (x,y) over the line y = x, the coordinates swap. So, if C(-1,-5) is reflected over y = x, the new - point C' has coordinates (-5,-1).

Step2: Reflect C'(-5,-1) over y = 1

The distance between y = - 1 and y = 1 is \(d=1-(-1)=2\). The new y - coordinate of the reflected point is \(y = 1+(1 - (-1))=3\), and the x - coordinate remains the same. So the point after reflection over y = 1 is (-5,3).

Step3: Reflect (-5,3) over x=-5

Since the x - coordinate of the point (-5,3) is the same as the equation of the line x=-5, the point remains unchanged after reflection over the line x = - 5.

Answer:

(-5,3)