Question

If quadrilateral RESP is is reflected across the line y = 2x +7 and again across the line y = -12x + 5, what will be the resulting image?
A. The resulting image will be a translation of the pre-image
B. The resulting image will be a rotation of the pre-image
C. The resulting image will be a reflection of the pre-image
D. The resulting image cannot be determined

Answer 1

The first reflection reverses the orientation and alters the direction of the vectors representing the sides of the quadrilateral. The second reflection does the same thing. The end result is that the orientation is unchanged by two reflections, and the direction of the sides of the quadrilateral is changed.

The appropriate choice is ...

... B. The resulting image will be a rotation of the pre-image.

_____

The center of rotation will be the point where the lines cross. (That is the invariant point.)

In the attachment, the green quadrilateral RESP is reflected across the line y=2x+7 (blue) to form the blue quadrilateral R'E'S'P'. That is then reflected across the line y = -12x +5 (orange) to give the orange quadrilateral R"E"S"P", which is a rotation of the pre-image.

The amount of rotation is double the angle between the lines, about 62.7°.