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

For a point $(x,y)$ reflected across the line $x = a$, the new $x$-coordinate is $2a - x$ and the $y$-coordinate remains the same. Here $a = 3$.

Step2: Assume coordinates of polygon

Let's assume $E(x_E,y_E)$, $F(x_F,y_F)$, $G(x_G,y_G)$, $H(x_H,y_H)$. After reflection, the new coordinates will be $E'(2\times3 - x_E,y_E)$, $F'(2\times3 - x_F,y_F)$, $G'(2\times3 - x_G,y_G)$, $H'(2\times3 - x_H,y_H)$.

Step3: Calculate new coordinates

Suppose $E(5,1)$, then $E'(2\times3 - 5,1)=(1,1)$. Suppose $F(3,2)$, then $F'(2\times3 - 3,2)=(3,2)$. Suppose $G(3,4)$, then $G'(2\times3 - 3,4)=(3,4)$. Suppose $H(5,3)$, then $H'(2\times3 - 5,3)=(1,3)$.

Answer:

The coordinates of the image polygon $E'F'G'H'$ are $E'(1,1)$, $F'(3,2)$, $G'(3,4)$, $H'(1,3)$ (assuming the original coordinates as above - actual coordinates depend on the real - values from the graph). To graph, plot the original polygon $EFGH$, draw the line $x = 3$, and then plot the new polygon $E'F'G'H'$ with the calculated coordinates.