Question

RST with vertices R (-2, -2) , S (-3, 1) , and T (1, 1) is translated by

(x, y) →
(x - 1, y + 3) . Then the image,
RST , is translated by

(x, y) →
(x + 4, y - 1) , resulting in
R "S"T ".
a. Find the coordinates for the vertices of
R "S"T ".

Answer 1

so we are doing:

(x,y) --->(x-1, y+3) ----> (x+4, y-1)

so for R(-2,-2)

(-2,-2) --->(-3, 1) ----> (1, 0)

do the same for the other points

(I am not sure why you have quotations around S and T in the final result. Are you saying that only S and T are transformed?
If so, then just apply the above to S and T, leaving R alone. If this had been my question , I would expect you to translate all 3 points, even have you graph the original, the intermediate and the final to show that congruency is maintained)