Question

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

Explanation:

Step1: Recall reflection formula

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 vertices

Let's assume $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$, $D(x_4,y_4)$. Suppose $A(1,3)$, $B(- 1,1)$, $C(-1,-2)$, $D(1,-3)$.

Step3: Calculate new x - coordinates

For point $A$: $x'_1=2\times3 - 1=5$, $y'_1 = 3$.
For point $B$: $x'_2=2\times3-(-1)=7$, $y'_2 = 1$.
For point $C$: $x'_3=2\times3-(-1)=7$, $y'_3=-2$.
For point $D$: $x'_4=2\times3 - 1=5$, $y'_4=-3$.

Answer:

The coordinates of the image of $A$ are $(5,3)$, of $B$ are $(7,1)$, of $C$ are $(7,-2)$ and of $D$ are $(5,-3)$.