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=
𝑥
=
and y=
𝑦
=
. the quadrilateral is ABCD. A(-4,3), B(5,3), C(5,-2), D(-4,-2)

Answer 1

so is it 0.5??

Answer 2

To find the lines of reflection that will flip the quadrilateral ABCD onto itself, we can analyze the coordinates of the vertices:

- A(-4, 3)
- B(5, 3)
- C(5, -2)
- D(-4, -2)

### Step 1: Identify the midpoints
We can find the midpoints of opposite sides to help identify the lines of symmetry.

For side AB:
- Midpoint (M1) = \(\left(\frac{-4 + 5}{2}, \frac{3 + 3}{2}\right) = \left(\frac{1}{2}, 3\right)\)

For side CD:
- Midpoint (M2) = \(\left(\frac{5 + -4}{2}, \frac{-2 + -2}{2}\right) = \left(\frac{1}{2}, -2\right)\)

The midpoint between AB and CD can be seen to be directly vertical. There will be a line of reflection at \(x = 0.5\) (the average of the x-coordinates of the midpoints of AB and CD).

### Step 2: Find the additional line of reflection
Next, we look at the midpoints of sides AD and BC:

For side AD:
- Midpoint (M3) = \(\left(\frac{-4 + -4}{2}, \frac{3 + -2}{2}\right) = (-4, \frac{1}{2})\)

For side BC:
- Midpoint (M4) = \(\left(\frac{5 + 5}{2}, \frac{3 + -2}{2}\right) = (5, \frac{1}{2})\)

This indicates a line of reflection that is horizontal, which will be found directly between the y-coordinates of M3 and M4. Since both midpoints share the same \(y\) coordinate, the midpoint is at \(y = 0.5\).

### Final Lines of Reflection
Thus, we conclude that the lines of reflection for the quadrilateral that will flip it onto itself are:
- \(x = \frac{1}{2}\)
- \(y = \frac{1}{2}\)

#### Answer:
The lines of reflection are:
\(x = \frac{1}{2}\) and \(y = \frac{1}{2}\).

Answer 3

Apologies for any confusion. Yes, \(0.5\) is the decimal representation of \(\frac{1}{2}\).

So, the lines of reflection can be expressed as:

- \(x = 0.5\)
- \(y = 0.5\)

To summarize:

The lines of reflection are:
- \(x = 0.5\)
- \(y = 0.5\)

Both values are equivalent, just expressed in different forms (fraction vs. decimal). Thank you for your patience!