Question

Given quadrilateral P (-3, 2) Q (3, -1) R (3, -4) S (-3, -7) in the diagram, find a line of reflection that will flip the figure onto itself.

One line of reflection is y = __

Answer 1

To find a line of reflection that will map the quadrilateral P (-3, 2), Q (3, -1), R (3, -4), S (-3, -7) onto itself, we can analyze the positions of the points.

First, let's calculate the midpoints of opposite sides or diagonals to find potential lines of symmetry.

1. The coordinates of points P and S are P (-3, 2) and S (-3, -7). The line connecting P and S is vertical.
2. The coordinates of points Q and R are Q (3, -1) and R (3, -4). This line connecting Q and R is also vertical.

### Step 1: Check the midpoints

**Midpoint of PS:**
Midpoint (M1) = \(\left(\frac{-3 + (-3)}{2}, \frac{2 + (-7)}{2}\right) = \left(-3, \frac{-5}{2}\right) = \left(-3, -2.5\right)\)

**Midpoint of QR:**
Midpoint (M2) = \(\left(\frac{3 + 3}{2}, \frac{-1 + (-4)}{2}\right) = \left(3, \frac{-5}{2}\right) = \left(3, -2.5\right)\)

### Step 2: Identify a line of reflection

Since both midpoints M1 and M2 lie on the line \(y = -2.5\), this is a horizontal line that could be a line of reflection for the quadrilateral.

### Therefore, the line of reflection is:
y = -2.5.

Thus, the correct answer is:
y = -2.5.