Question

answer all parts of the question on the graph to the right. plot the pre - image and label it appropriately. make sure to show the transformations using different colors and labeling them appropriately. show the line of reflection when reflecting.

• plot the pre - image, quadrilateral abcd: a(-6,4), b(-5,6), c(-4,4), d(-5,2).

• then, reflect the quadrilateral across the line x = -2 creating image abcd.

• then, translate the image abcd (x,y)→(x + 3,y - 5) to create image a\b\c\d\.

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 $a=-2$.
For point $A(-6,4)$:
$x'=2\times(-2)-(-6)=2$, $y' = 4$, so $A'=(2,4)$
For point $B(-5,6)$:
$x'=2\times(-2)-(-5)=1$, $y' = 6$, so $B'=(1,6)$
For point $C(-4,4)$:
$x'=2\times(-2)-(-4)=0$, $y' = 4$, so $C'=(0,4)$
For point $D(-5,2)$:
$x'=2\times(-2)-(-5)=1$, $y' = 2$, so $D'=(1,2)$

Step2: Apply translation rule

The translation rule is $(x,y)\to(x + 3,y - 5)$.
For point $A'(2,4)$:
$x''=2 + 3=5$, $y''=4-5=-1$, so $A''=(5,-1)$
For point $B'(1,6)$:
$x''=1 + 3=4$, $y''=6-5 = 1$, so $B''=(4,1)$
For point $C'(0,4)$:
$x''=0 + 3=3$, $y''=4-5=-1$, so $C''=(3,-1)$
For point $D'(1,2)$:
$x''=1 + 3=4$, $y''=2-5=-3$, so $D''=(4,-3)$

Answer:

$A''(5,-1)$, $B''(4,1)$, $C''(3,-1)$, $D''(4,-3)$