Question

1. for each point (x,y), find its image under the transformation (x + 12,y - 2)

a. a=(-10,8)
b. b=(-4,9)
c. c=(-2,6)

1. sketch △abc and its image on the grid
2. describe the transformation (x,y)→(x + 12,y - 2) in words

Explanation:

Step1: Apply transformation to point A

For point $A=(-10,8)$, the transformation $(x,y)\to(x + 12,y - 2)$ gives:
$x=-10+12 = 2$
$y=8 - 2=6$
So the image of $A$ is $(2,6)$.

Step2: Apply transformation to point B

For point $B=(-4,9)$, the transformation $(x,y)\to(x + 12,y - 2)$ gives:
$x=-4+12 = 8$
$y=9 - 2 = 7$
So the image of $B$ is $(8,7)$.

Step3: Apply transformation to point C

For point $C=(-2,6)$, the transformation $(x,y)\to(x + 12,y - 2)$ gives:
$x=-2+12 = 10$
$y=6 - 2 = 4$
So the image of $C$ is $(10,4)$.

Step4: Describe the transformation

The transformation $(x,y)\to(x + 12,y - 2)$ means a translation 12 units to the right (because we add 12 to the $x$-coordinate) and 2 units down (because we subtract 2 from the $y$-coordinate).

Answer:

1.

• Image of $A$: $(2,6)$
• Image of $B$: $(8,7)$
• Image of $C$: $(10,4)$

1. The transformation is a translation 12 units to the right and 2 units down.