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 flips a figure onto itself. For a polygon on a coordinate - plane, we check the position of its vertices.

Step2: Analyze the x - coordinate of vertices

The x - coordinate of point $W$ is $- 2$ and of point $A$ is $8$. The mid - point of the line segment joining $W$ and $A$ is $\frac{-2 + 8}{2}=3$. The x - coordinate of point $D$ is $-2$ and of point $R$ is $8$. The mid - point of the line segment joining $D$ and $R$ is also $\frac{-2 + 8}{2}=3$.

Step3: Determine the line of symmetry

The vertical line $x = 3$ will flip the polygon onto itself because for every point $(x,y)$ on the polygon, there is a corresponding point $(6 - x,y)$ (since the distance from $x$ to $3$ is the same as the distance from $6 - x$ to $3$) on the other side of the line $x = 3$.

Answer:

$x = 3$