The vertices of a triangle are a(4,5), b(7,1), and (9,6). after reflecting over the line x = 5, what are the new coordinates?

A'(6,5),  B'(3,1) and C'(1,6)

Step-by-step explanation:

The reflection of a given point over the line x = 5 doesn't change its y- coordinate.

The distance from the original point to the line must be the same as from the reflected point to the line, then:

distance from A(4,5) to x = 5 is 5-4 = 1, then the x-coordinate of A' is 5+1 = 6

distance from B(7,1) to x = 5 is 7-5 = 2, then the x-coordinate of B' is 5-2 = 3

distance from C(9,6) to x = 5 is 9-5 = 4, then the x-coordinate of C' is 5-4 = 1

Therefore, the reflected points are: A'(6,5),  B'(3,1) and C'(1,6)