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=___ .

Answer 1

The coordinates of ABCD are, (-4,3) (5,3) (5,-2) (-4,-2)

Answer 2

To provide an accurate response, I need to know the specific figure being referred to and its position on the coordinate plane. Generally, in problems involving reflections, the lines of reflection can often be vertical (like \(x = a\)) and horizontal (like \(y = b\)), depending on the symmetry of the figure.

If you provide the coordinates or a description of the figure, I can help determine the lines of reflection that would flip the figure onto itself.

Answer 3

To determine the lines of reflection that will flip the quadrilateral ABCD (whose vertices are at the coordinates A(-4,3), B(5,3), C(5,-2), and D(-4,-2)) onto itself, we can analyze the figure.

### Step 1: Identify the Center of the Figure
The vertices indicate that the quadrilateral is a rectangle, since opposite sides are equal and parallel. We can find the center of the rectangle by averaging the x-coordinates and y-coordinates:

- \(x\)-coordinates: \((-4 + 5) / 2 = 0.5\)
- \(y\)-coordinates: \((3 + (-2)) / 2 = 0.5\)

The center of the rectangle is at (0.5, 0.5).

### Step 2: Determine the Lines of Reflection
1. **Vertical Line of Reflection**:
- The line of reflection that divides the rectangle vertically will be the vertical line that passes through its center.
- Since the center's x-coordinate is 0.5, the line of reflection is:
\[
x = 0.5
\]

2. **Horizontal Line of Reflection**:
- The line of reflection that divides the rectangle horizontally will pass through the center's y-coordinate.
- Since the center's y-coordinate is also 0.5, the line of reflection is:
\[
y = 0.5
\]

### Conclusion
Thus, the lines of reflection that will flip the quadrilateral ABCD onto itself are:
\[
\text{x} = 0.5 \quad \text{and} \quad \text{y} = 0.5
\]