Question

A quadrilateral has vertices (0,0)
, (−8,0)
, (0,−6)
and (−8,−6)
Complete the equation with the vertical line of symmetry that will carry the quadrilateral onto itself.(1 point)

Answer 1

Which statement best summarizes the rotations that turn a square onto itself?(1 point)
Responses

A square will rotate onto itself after 90-degree, 180-degree, 270-degree, and 360-degree rotations.
A square will rotate onto itself after 90-degree, 180-degree, 270-degree, and 360-degree rotations.

A square will rotate onto itself after a 180-degree rotation.
A square will rotate onto itself after a 180-degree rotation.

A square will rotate onto itself after a 90-degree or 180-degree rotation.
A square will rotate onto itself after a 90-degree or 180-degree rotation.

A square will rotate onto itself after a 90-degree rotation.

Answer 2

To find the equation of the vertical line of symmetry, we can compute the average of the x-coordinates of the opposite vertices of the quadrilateral.

The opposite vertices of the quadrilateral are (0, 0) and (-8, 0), which have x-coordinates of 0 and -8, respectively. The average of these x-coordinates is (0 + (-8)) / 2 = -4.

Therefore, the equation of the vertical line of symmetry is x = -4.

Answer 3

A square will rotate onto itself after a 90-degree, 180-degree, 270-degree, and 360-degree rotations.