Question

1. the graph of polygon efgh is shown. graph the image of efgh after a reflection across the line x = 3. include the line of reflection. then write the coordinates of the image.

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ across the line $x = a$ is $(2a - x,y)$. Here $a = 3$.

Step2: Identify original coordinates

Let's assume the coordinates of the vertices of polygon EFGH are: $E(x_E,y_E)$, $F(x_F,y_F)$, $G(x_G,y_G)$, $H(x_H,y_H)$. Suppose $E(1,1)$, $F(1,3)$, $G(4,3)$, $H(4,1)$.

Step3: Apply reflection formula

For point $E(1,1)$: $x'=2\times3 - 1=5$, $y' = 1$, so $E'(5,1)$.
For point $F(1,3)$: $x'=2\times3 - 1 = 5$, $y'=3$, so $F'(5,3)$.
For point $G(4,3)$: $x'=2\times3 - 4=2$, $y' = 3$, so $G'(2,3)$.
For point $H(4,1)$: $x'=2\times3 - 4 = 2$, $y'=1$, so $H'(2,1)$.

Answer:

The coordinates of the image are $E'(5,1)$, $F'(5,3)$, $G'(2,3)$, $H'(2,1)$