Asequence 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′.

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'.

x=half

step-by-step explanation: