Question

Suppose the equation of line t is y = x. Which shows the graph of ΔA'B'C' for Rt? Triangle A B C graphed on a coordinate plane with vertices at A negative 1 comma 1, B 1 comma negative 1, and C negative 3 comma negative 1. Group of answer choices Triangle A prime B prime C prime graphed on a coordinate plane with vertices at A prime 1 comma negative 1, B prime 3 comma negative 1, and C prime negative 1 comma negative 3. Triangle A prime B prime C prime graphed on a coordinate plane with vertices at A prime 1 comma negative 1, B prime 2 comma negative 1, and C prime negative 1 comma negative 3. Triangle A prime B prime C prime graphed on a coordinate plane with vertices at A prime 1 comma negative 1, B prime negative 1 comma 1, and C prime negative 1 comma negative 3. Triangle A prime B prime C prime graphed on a coordinate plane with vertices at A prime negative 3 comma negative 1, B prime negative 1 comma 2, and C prime negative 3 comma negative 5.

Answer 1

Answer:

The correct option is;

Triangle A prime B prime C prime graphed on a coordinate plane with vertices at A prime 1 comma negative 1, B prime negative 1 comma 1, and C prime negative 1 comma negative 3

Step-by-step explanation:

The given parameters are;

The equation of the line t over which ΔABC is reflected is given by y = x

The coordinates of the vertices of ΔABC are given as follows;

A(-1, 1), B(1, -1), and C(-3, -1)

The reflection of a preimage (x, y) across the line y = x gives an image with coordinates at (y,  x)

Therefore, the coordinates of the vertices of the image ΔA'B'C' after the reflection of the preimage ΔABC over the line, y = x are given as follows;

Coordinates of preimage → Reflection across y = x → Coordinates of image

A(-1, 1) ${}$                       Reflection across the line y = x          A'(1, -1)

B(1, -1) ${}$                       Reflection across the line y = x          B'(-1, 1)

C(-3, -1) ${}$                     Reflection across the line y = x          C'(-1, -3)

Therefore, the correct option is triangle A prime B prime C prime graphed on a coordinate plane with vertices at A prime 1 comma negative 1, B prime negative 1 comma 1, and C prime negative 1 comma negative 3.