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)
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.
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.
A square will rotate onto itself after a 90-degree, 180-degree, 270-degree, and 360-degree rotations.
To determine the equation of the vertical line of symmetry for the given quadrilateral, we need to find the x-coordinate of the line that passes through the midpoint of the top and bottom sides.
First, let's find the coordinates of the midpoint of the top side. The top side has vertices (0, 0) and (-8, 0). The x-coordinate of the midpoint is the average of the x-coordinates of these two points, which is:
(0 + (-8)) / 2 = -4
So, the midpoint of the top side is (-4, 0).
Next, let's find the coordinates of the midpoint of the bottom side. The bottom side has vertices (0, -6) and (-8, -6). The x-coordinate of the midpoint is the average of the x-coordinates of these two points, which is:
(0 + (-8)) / 2 = -4
So, the midpoint of the bottom side is also (-4, -6).
Since the x-coordinate of both midpoints is the same, the equation of the vertical line of symmetry is:
x = -4
The equation x = -4 represents a vertical line passing through (-4, 0) and (-4, -6), which will carry the quadrilateral onto itself when reflected across this line.