Question

Image included: A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the ________ followed by a translation ________.

first box is a-(x-axis) b- (y-axis) c-(line y=x) or d-(line y=-x)
second box is a-(8 units to the right 10 units up) b- (8 units to the right 4 units up) c-(10 units to the right 2 units up) or d-(10 units to the right 4 units up)

Answer 1

First is the y=x line, second is 10 to the right, 4 up.

Answer 2

The answer is (1) y = x and (2) 10 units to the right and 4 units up.

Explanation:

A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC to ∆A′B′C′ is a reflection across the line y = x followed by a translation 10 units to the right and 4 units up.

The first is a reflection across a line and second is a translation.

We can see that the co-ordinates of point C are (-4, -2).

After reflection from the line y = x, the co-ordinates becomes (2, -4).

And the coordinates of point C' are (12, 0). So, to reach point C' from point C, we have to add 10 units to the x-coordinate and 4 units to the y-coordinate.

That makes a translation of 10 units right and 4 units up.