Question

Using the transformation T : (x, y) → (x + 2, y + 1), find the distance named Find C'A'

Answer 1

We have that
A' (2,1)

C(-2,2)-------> Using the transformation-----> C' (-2+2,2+1)----> C' (0,3)

with 
A' (2,1) and C' (0,3)
find the distance C'A'

d=√[(y2-y1)²+(x2-x1)²]----> d=√[(3-1)²+(0-2)²]----> d=√8----> 2√2 units

the answer is
the distance C'A' is 2√2 units