Question

Rectangle upper A upper B upper C upper D is plotted on a coordinate plane.
Complete the equations identifying both lines of reflection that will flip the given figure onto itself.

(1 point)
The lines of reflection are x= and y=.

Answer 1

To determine the lines of reflection that will flip rectangle ABCD onto itself, we need to consider the properties of the rectangle.

1. Since rectangles are symmetrical:
- There will be a vertical line of reflection that bisects the rectangle vertically, which typically occurs at the x-coordinate of the midpoint of the left and right sides of the rectangle.
- There will also be a horizontal line of reflection that bisects the rectangle horizontally, which typically occurs at the y-coordinate of the midpoint of the top and bottom sides of the rectangle.

Assuming the rectangle is aligned with the axes, the lines of reflection can generally be expressed as:

- For the vertical reflection line: \(x = m\), where \(m\) is the x-coordinate of the midpoint between the left and right sides.
- For the horizontal reflection line: \(y = n\), where \(n\) is the y-coordinate of the midpoint between the top and bottom sides.

To provide specific answers, we would need the coordinates of the vertices of the rectangle. However, you can generalize the answers as follows:

**The lines of reflection are**:

- \(x = \text{(x-coordinate of the midpoint)}\)
- \(y = \text{(y-coordinate of the midpoint)}\)

If the rectangle's vertices were provided with specific coordinates, we could calculate the midpoint coordinates to give exact equations.