Question

name the type of transformation shown:
1.
2.
3.
4.

1. figure abc has vertices a(-3,3), b(1, - 1), and c(0,5). sketch abc and draw its image after the translation (x,y)→(x + 4,y + 2).
2. figure abc has vertices a(4,2), b(2,6), and c(6,6). sketch abc and draw its image after the translation (x,y)→(x - 6,y - 3).

use coordinate - notation to describe the translation.

1. 5 units to the right, 3 units down
2. 9 units to the left, 7 units up

Explanation:

Step1: Identify transformation type

For questions 1 - 4, observe the movement of the shapes on the coordinate - grid. If a shape moves without rotation or reflection, it is a translation.

Step2: Sketch and find image for question 5

Given vertices of $\triangle ABC$: $A(-3,3)$, $B(1, - 1)$, $C(0,5)$ and translation $(x,y)\to(x + 4,y + 2)$.
For point $A$: $x=-3,y = 3$, new $x=-3 + 4=1$, new $y=3 + 2 = 5$, so $A'=(1,5)$.
For point $B$: $x = 1,y=-1$, new $x=1 + 4=5$, new $y=-1+2 = 1$, so $B'=(5,1)$.
For point $C$: $x = 0,y = 5$, new $x=0 + 4=4$, new $y=5 + 2=7$, so $C'=(4,7)$. Sketch $\triangle ABC$ and $\triangle A'B'C'$.

Step3: Sketch and find image for question 6

Given vertices of $\triangle ABC$: $A(4,2)$, $B(2,6)$, $C(6,6)$ and translation $(x,y)\to(x - 6,y - 3)$.
For point $A$: $x = 4,y = 2$, new $x=4-6=-2$, new $y=2 - 3=-1$, so $A'=(-2,-1)$.
For point $B$: $x = 2,y = 6$, new $x=2-6=-4$, new $y=6 - 3=3$, so $B'=(-4,3)$.
For point $C$: $x = 6,y = 6$, new $x=6-6 = 0$, new $y=6 - 3=3$, so $C'=(0,3)$. Sketch $\triangle ABC$ and $\triangle A'B'C'$.

Step4: Write coordinate - notation for question 9

5 units to the right means $x\to x + 5$, 3 units down means $y\to y-3$. The translation is $(x,y)\to(x + 5,y - 3)$.

Step5: Write coordinate - notation for question 10

9 units to the left means $x\to x-9$, 7 units up means $y\to y + 7$. The translation is $(x,y)\to(x - 9,y + 7)$.

Answer:

1 - 4: Translation.
5: $A'=(1,5),B'=(5,1),C'=(4,7)$ (after sketching $\triangle ABC$ and $\triangle A'B'C'$).
6: $A'=(-2,-1),B'=(-4,3),C'=(0,3)$ (after sketching $\triangle ABC$ and $\triangle A'B'C'$).
9: $(x,y)\to(x + 5,y - 3)$.
10: $(x,y)\to(x - 9,y + 7)$.