Question

1. wxyz is a trapezoid with vertices w(-1,2), x(3,2), y(5,-1), and z(-3,-1). which of the following best describes a line of symmetry for the trapezoid? (try graphing the trapezoid on your graph paper) both x = 1 and y = 1/2 are lines of symmetry. the line of symmetry is x = 1 because it connects the midpoints of wx and zy. the trapezoid has no lines of symmetry. the line of symmetry is y = 1/2 because it connects the midpoints of wx and zy.

Explanation:

Step1: Find mid - point of $\overline{WX}$

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 $W(-1,2)$ and $X(3,2)$, $x=\frac{-1 + 3}{2}=1$, $y=\frac{2+2}{2}=2$. The mid - point of $\overline{WX}$ is $(1,2)$.

Step2: Find mid - point of $\overline{ZY}$

For $Z(-3,-1)$ and $Y(5,-1)$, $x=\frac{-3 + 5}{2}=1$, $y=\frac{-1-1}{2}=-1$. The mid - point of $\overline{ZY}$ is $(1,-1)$.

Step3: Analyze the line of symmetry

The line passing through the mid - points of $\overline{WX}$ and $\overline{ZY}$ is $x = 1$. When we reflect the trapezoid $WXYZ$ across the line $x = 1$, the two halves of the trapezoid match up. The line $y=\frac{1}{2}$ is not a line of symmetry for this trapezoid.

Answer:

The line of symmetry is $x = 1$ because it connects the midpoints of $\overline{WX}$ and $\overline{ZY}$.