Question

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

A 3,-4
B 3,5
D 3,-2
C 3,-2
They all connect and make a square shape

Answer 1

To identify the lines of reflection that will flip the given coordinates onto themselves, we first note that the points provided suggest a square shape.

The points listed are:
- A (3, -4)
- B (3, 5)
- C (3, -2)
- D (3, -2)

However, it seems that point C is listed twice. Assuming you meant to have four unique points that form a square, let's clarify the reflection lines based on this shape.

Given that three of the points have an x-coordinate of 3, it appears this square is vertically oriented. Here are the possible lines of reflection:

1. **Vertical Line of Reflection:** The vertical line of reflection would be the vertical line that bisects the square. This would be at \(x = 3\).

2. **Horizontal Line of Reflection:** The horizontal line of reflection would be the horizontal line that bisects the square. This would be the average of the y-coordinates of the topmost and bottommost points.

Since the coordinates indicate:
- The lowest point A is at \(y = -4\).
- The highest point B is at \(y = 5\).

The midpoint for the y-coordinates is calculated as follows:
\[
y_{\text{mid}} = \frac{-4 + 5}{2} = \frac{1}{2}
\]

Therefore, the horizontal line of reflection is at \(y = \frac{1}{2}\).

So the completed statement would be:
The lines of reflection are **x = 3** and **y = 1/2**.