Question

examine the polygon in the figure shown. identify a line of symmetry that will flip the figure onto itself. (1 point) y - axis x - axis y = 3 x = 3

Explanation:

Step1: Recall line - symmetry concept

A line of symmetry divides a figure into two congruent parts such that one part is the mirror - image of the other.

Step2: Analyze each option

• For the y - axis ($x = 0$): The points on the left - hand side of the y - axis do not match up with the points on the right - hand side when reflected over the y - axis.
• For the x - axis ($y = 0$): The points above the x - axis do not match up with the points below the x - axis when reflected over the x - axis.
• For the line $y = 3$: The figure is not symmetric about the line $y = 3$.
• For the line $x=3$: The distance of point $W(-2,5)$ from $x = 3$ is $| - 2-3|=5$, and the distance of point $A(8,5)$ from $x = 3$ is $|8 - 3| = 5$. The distance of point $D(-2,-1)$ from $x = 3$ is $| - 2-3|=5$, and the distance of point $R(8,-1)$ from $x = 3$ is $|8 - 3|=5$. When the figure is reflected over the line $x = 3$, the left - hand side and the right - hand side of the figure will coincide.

Answer:

$x = 3$