What is the image point of (-5,-6)(−5,−6) after the transformation T_{3,-1}\circ R_{270^{\circ}}T 3,−1 ​ ∘R 270 ∘ ​ ?

Question

What is the image point of (−5,−6) after the transformation T3,−1​∘R270∘​?

Answer 1

Do the translation first. The rule is:

T(3,-1)

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

Do the rotation second. Assuming it's about the origin (O), the rule is:

R(270 CW,O)

(x,y) -------------------> (-y,x)

Only you want to do it on the translated coordinates:

R(270 CW,O)

(x+3,y-1) -------------------> (-(y-1), x+3) This is the answer. Plug in (-5,-6) for (x,y).