Question

What set of reflections would carry parallelogram ABCD onto itself? Parallelogram ABCD is shown. A is at negative 5, 1. B is at negative 4, 3. C is at negative 1, 3. D is at negative 2, 1.

Answer 1

Okay, y-axis, x-axis, y-axis, x-axis will be your answer. Take point (-5, 1): Reflect across y-axis: (5, 1) Reflect across x-axis: (5, -1) Reflect across y-axis: (-5, -1) Reflect across x-axis: (-5, 1) So that's the correct answer, because it brings you back to (-5, 1).

Answer 2

Answer:

1. As parallelogram have no line of symmetry, so  after no rotation we can get a parallelogram which is mapped onto itself.

2. Now if we reflect the parallelogram ABCD along + Y axis

3.   If we reflect the parallelogram ABCD along -X axis

4.   If we reflect the parallelogram ABCD along  the line , y=x

 In all the three cases mentioned above i.e 2,3,and 4 we are getting a parallelogram congruent to ABCD.