Question

Complete the equations identifying both lines of reflection that will flip the given figure onto itself.A is(3,4) B is (3,5) C is ( 5,-2) and D is (-4,-2)
(1 point)
The lines of reflection are x =
and y=

Answer 1

To identify the lines of reflection that will flip the figure formed by points A(3,4), B(3,5), C(5,-2), and D(-4,-2) onto itself, we need to find the lines of symmetry of the shape formed by these points.

1. **Vertical Line of Reflection**:
The x-coordinates of points A and B are the same (3), while points C and D have different x-coordinates. However, we can observe that the reflections over a vertical line would require us to find the midpoint of the x-coordinates.

The x-coordinates of A, B, and D are 3, -4 respectively.
The average (midpoint) of the x-coordinates will determine the vertical line of reflection:

\[
\text{Midpoint } x = \frac{3 + (-4)}{2} = \frac{-1}{2}
\]

Thus, the vertical line of reflection is \(x = -\frac{1}{2}\).

2. **Horizontal Line of Reflection**:
To find the horizontal line of reflection, we should consider the average of the y-coordinates of points A, B, C, and D.

The y-coordinates are: 4 (A), 5 (B), -2 (C), and -2 (D).
The average (midpoint) of the y-coordinates will be:

\[
\text{Midpoint } y = \frac{4 + 5 + (-2) + (-2)}{4} = \frac{5}{4} = 1.25
\]

Thus, the horizontal line of reflection is \(y = 1.25\).

So, the lines of reflection that will flip the figure onto itself are:

\[
\boxed{x = -\frac{1}{2}} \quad \text{and} \quad \boxed{y = 1.25}
\]