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 $y=square$

Explanation:

Step1: Identify mid - point of vertical sides

The vertical sides are between points with the same x - coordinates. For the left - hand side with points $P(-3,2)$ and $S(-3, - 7)$, and the right - hand side with points $Q(3,-1)$ and $R(3,-4)$. The mid - point of the vertical distance between $P$ and $S$ is $\frac{2+( - 7)}{2}=\frac{2 - 7}{2}=-\frac{5}{2}=-2.5$, and the mid - point of the vertical distance between $Q$ and $R$ is $\frac{-1+( - 4)}{2}=\frac{-1 - 4}{2}=-\frac{5}{2}=-2.5$.

Step2: Determine line of reflection

A line of reflection that flips the figure onto itself is a horizontal line passing through the mid - point of the vertical distances of the figure. The equation of a horizontal line is of the form $y = k$, where $k$ is a constant. Since the mid - point of the vertical distances is at $y=-2.5$, the line of reflection is $y=-2.5$.

Answer:

$y = - 2.5$