Question

A sequence of transformations maps ∆ABC onto ∆A″B″C″. The type of transformation that maps ∆ABC onto ∆A′B′C′ is a

reflection
.

When ∆A′B′C′ is reflected across the line x = -2 to form ∆A″B″C″, vertex _____
of ∆A″B″C″ will have the same coordinates as B′.

Answer 1

The transformation that maps ΔABC onto ΔA'B'C' is a reflection across the x-axis (or across the line y = 0).

When ΔA'B'C' is reflected across the line x = -2 (shown in the figure) to form ΔA"B"C", the vertex of ΔA"B"C" will have the same coordinates as B', which is (-2,-6)

Answer 2

The type of transformation that maps ∆ABC onto ∆A′B′C′ is a reflection across x-axis, we can deduct this from the image attached. We observe that the figure is reflected like a mirror across the horizontal axis, which is x-axis, or the line y = 0.

When ∆A′B′C′ is reflected across the line x = -2 to form ∆A″B″C″, vertex B''

of ∆A″B″C″ will have the same coordinates as B′. If we observe closer, we see that in the ∆A′B′C′ vertex B' has coordinates (-2;-6). So, if we reflect this figure across x = -2, the vertex B' will be like a pivot point, it won't move, because we are translated around that x-value. Therefore vertex B'' will be the same as B'.