Suppose m is the line with equation y = −4 and ΔA'B'C is mapped to ΔA"B"C" by applying the glide reflection T3, 0 Rm. What are the coordinates of ΔA″B″C″?

The coordinates of ΔA''B''C'' are;

A''(-1, -3), B''(-2, -6), C''(1 , -7)

Step-by-step explanation:

A glide reflection involves the reflection of the preimage over a given line, followed by the translation of the resulting image along the given line

Given that the coordinates of the triangle ΔA'B'C' are;

A'(-4, -5), B'(-5, -2), C'(-2, -1), we have by reflection across the line y = -4

A''(-4, -4 + 1) = A''(-4, -3)

B''(-5, -4 - 2) = B''(-5, -6)

C''(-2, -4-3) = C''(-2, -7)

Translation of A''B''C'' by T 3, 0, we have;

A''(-4, -3)  → T₃, ₀ → A''(-4 + 3, -3) = A''(-1, -3)

B''(-5, -6)  → T₃, ₀ → B''(-5 + 3, -6) = B''(-2, -6)

C''(-2, -7) → T₃, ₀ → C''(-2 + 3, -7) = C''(1 , -7)

The coordinates of ΔA''B''C'' are therefore;

A''(-1, -3), B''(-2, -6), C''(1 , -7).