What is the image point of (-3,-5)(−3,−5) after the transformation T_{2,1}\circ D_{2}T 2,1 ​ ∘D 2 ​ ?

Answer 1

Let's assume point (-3,-5) is Point P.

Step 1: Translate point P(-3,-5) to P' (2 units right and 1 unit up).

Do the translation first and Dilation later.

Translation rule is:

T(2,1)

P(x,y) -------------------> P'(x+2,y+1)

T(2,,1)

P(-3,-5) ------------------->P'(-3+2,-5+1) = P'(-1,-4)

Step 2: Dilation 2 times. Dilate point P' to P" (2 times)

Dilation rule is:

D(2)

P'(x,y) -------------------> P"(x.2,y.1)

D(2)

P'(-1,-4) ------------------->P"(-2,-8)

Answer : Point (-2,-8)