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: Find mid - point of vertical segment

The vertical segment has endpoints $R(3,-4)$ and $S(-3,-7)$. The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For $R(3,-4)$ and $S(-3,-7)$, the $x$ - coordinate of the mid - point is $\frac{3+( - 3)}{2}=0$, and the $y$ - coordinate is $\frac{-4+( - 7)}{2}=\frac{-4 - 7}{2}=-\frac{11}{2}=-5.5$.

Step2: Determine line of reflection

A line of reflection that will flip the figure onto itself is the line that is the perpendicular bisector of the segment connecting corresponding points. Since the figure has vertical symmetry, the line of reflection is a horizontal line passing through the mid - point of the vertical segment between $R$ and $S$. The equation of a horizontal line is of the form $y = k$, where $k$ is the $y$ - coordinate of any point on the line. Here, $k=-5.5$.

Answer:

$y=-5.5$