Use the image to answer the question.

Question

Trapezoid upper P upper Q upper R upper S is plotted on a coordinate plane.

Image Long DescriptionThe values on both axes range from negative 10 to 10 in one-unit increments. The coordinates of the vertices of the trapezoid are as follows: upper P is left parenthesis negative 3 comma 2 right parenthesis, upper Q is left parenthesis 3 comma negative 1 right parenthesis, upper R is left parenthesis 3 comma negative 4 right parenthesis, and upper S is left parenthesis negative 3 comma negative 7 right parenthesis.

Given quadrilateral PQRS
in the diagram, find a line of reflection that will flip the figure onto itself.

(1 point)
One line of reflection is y =

.

Answer 1

To find a line of reflection that will flip the trapezoid PQRS onto itself, we can look for a line that bisects the opposite sides of the trapezoid or a line of symmetry.

The trapezoid has vertices at:

• P(-3, 2)
• Q(3, -1)
• R(3, -4)
• S(-3, -7)

Looking at the coordinates of points P and S, and points Q and R, we notice that the trapezoid has symmetry about the vertical line (the y-axis).

To confirm this, we can calculate the midpoints of the vertical segments connecting P to S and Q to R:

• Midpoint of PS: \[ \text{Midpoint PS} = \left( \frac{-3 + -3}{2}, \frac{2 + (-7)}{2} \right) = \left(-3, \frac{-5}{2}\right) \]
• Midpoint of QR: \[ \text{Midpoint QR} = \left( \frac{3 + 3}{2}, \frac{-1 + (-4)}{2} \right) = \left(3, \frac{-5}{2}\right) \]

Since both midpoints have the same y-coordinate, this confirms a vertical line of symmetry.

Therefore, one line of reflection that will flip trapezoid PQRS onto itself is the line: \[ y = -\frac{5}{2} \]

This is a line parallel to the x-axis passing through the y-coordinate -2.5.

Thus, the line of reflection is:

y = -2.5