Question

The parallelogram below will undergo a single transformation.

Which transformation will result in an image that is identical to the original parallelogram? Choose all that apply.

a reflection about x = -4
a reflection about y = 4.5
a rotation through an angle of 360° about the origin
a rotation through an angle of 360° about vertex R

Answer 1

The last 2 options are correct

Answer 2

The correct options are 3 and 4.

Explanation:

The vertices of the parallelogram are P(-8,6), Q(-2,6), R(0,-3) and S(-6,3).

If a figure reflected about x = -4, then

`(x,y)\rightarrow (-x-8,y)`

Therefore the image is not identical to the original parallelogram.

If a figure reflected about y = 4.5, then

`(x,y)\rightarrow (x,-y+9)`

Therefore the image is not identical to the original parallelogram.

If a figure rotated through an angle of 360° about the origin, then

`(x,y)\rightarrow (x,y)`

Therefore the image is identical to the original parallelogram.

If a figure rotated through an angle of 360° about the vertex R, then

`(x,y)\rightarrow (x,y)`

Therefore the image is identical to the original parallelogram.

Thus the correct options are 3 and 4.