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: Identify mid - points of vertical sides

For the vertical sides with endpoints $P(-3,2)$ and $S(-3, - 7)$, and $Q(3,-1)$ and $R(3,-4)$. 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 the points $P(-3,2)$ and $S(-3,-7)$, the mid - point is $(-3,\frac{2+( - 7)}{2})=(-3,-\frac{5}{2})$. For the points $Q(3,-1)$ and $R(3,-4)$, the mid - point is $(3,\frac{-1+( - 4)}{2})=(3,-\frac{5}{2})$.

Step2: Determine the line of reflection

The line passing through these mid - points is a horizontal line. The equation of a horizontal line is of the form $y = k$, where $k$ is the $y$ - coordinate of any point on the line. Since the $y$ - coordinate of the mid - points is $-\frac{5}{2}$, the line of reflection is $y=-\frac{5}{2}$.

Answer:

$y =-\frac{5}{2}$