Question

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 =

Explanation:

Step1: Observe the coordinates of the points

Points $P(-3,2)$ and $S(-3, - 7)$ have the same $x -$coordinate, and points $Q(3,-1)$ and $R(3,-4)$ have the same $x -$coordinate. The figure is symmetric about a horizontal line.

Step2: Find the mid - point of the vertical distance between corresponding points

For the vertical distance between $P$ and $S$, the $y -$coordinates are $y_1 = 2$ and $y_2=-7$. The mid - point of the $y -$values is $\frac{2+( - 7)}{2}=\frac{2 - 7}{2}=-\frac{5}{2}=-2.5$.
For the vertical distance between $Q$ and $R$, the $y -$coordinates are $y_3=-1$ and $y_4 = - 4$. The mid - point of these $y -$values is $\frac{-1+( - 4)}{2}=\frac{-1 - 4}{2}=-\frac{5}{2}=-2.5$.

Answer:

$y=-2.5$