Question

1. write the coordinates of the final image given: $(x, y) \

ightarrow (x + 2, y - 3)$, then rotate the new image $270^\circ$ counterclockwise

Explanation:

Step1: Identify original coordinates

Original points: $A(-5,1)$, $I(-1,2)$, $J(-5,6)$

Step2: Apply translation $(x,y)\to(x+2,y-3)$

For $A$: $(-5+2, 1-3)=(-3,-2)$
For $I$: $(-1+2, 2-3)=(1,-1)$
For $J$: $(-5+2, 6-3)=(-3,3)$

Step3: Apply 270° counterclockwise rotation

Rotation rule: $(x,y)\to(y,-x)$
For translated $A(-3,-2)$: $(-2, 3)$
For translated $I(1,-1)$: $(-1, -1)$
For translated $J(-3,3)$: $(3, 3)$

Answer:

Final coordinates: $A'(-2,3)$, $I'(-1,-1)$, $J'(3,3)$