Question

Which of the following symmetries apply to the isosceles trapezoid below?

Answer 1

Answer:

Reflective symmetry over the line y=-x

Step-by-step explanation:

This trapezoid is symmetrical around an axis defined by the line y=-x.

It is not, symmetric with an image of itself rotated by 90 degrees. Neither is it symmetric to an image obtained by reflection around -7x+1. These two statements can be easily verified by transforming one of its corner points and realizing they do not belong to the set of corners of the original trapezoid.

Answer 2

Answer: Only reflection across y=-x

Step-by-step explanation:

Line y=-x, slope -1 is perpendicular bisector of base running from (-8,1) to (-1,8), slope 1, and figure is isosceles trapezoid so even though the figure is cut off we know line is also perpendicular bisector of the other base.

Although (-8,1) rotates to (-1,8) about (-1,-1) through 90°, the other vertices don't. Always check more than one vertex.

If you draw some segments perpendicular to y=-7x+1, you see that the points on left do not map to points on right.