What are the coordinates of R' for the dilation D(0.5, P (PQRS)?

Three step process.

Step 1, convert Q, R, P, and S to coordinates measured from point P rather than from the origin by subtracting P from each point:

Q' = Q-P = (-3-(-3),2-(-3)) = (0,5)

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

P' = P-P = (-3-(-3),-3-(-3)) =(0,0)

S' = S-P = (1-(-3),-3-(-3)) = (4,0)

Step 2, Apply the dilation factor (0.5):

Q'' = (0.5)Q' = (0.5*0, 0.5*5) = (0,2.5)

R'' = (0.5)R' =

P''= (0.5)P' =

S''= (0.5)S' =

Step 3, Convert coordinates back to the origin (vice point P) by adding P to each point.  These are the dilated points.

Q''' = Q'' + P = (0+(-3),2.5+(-3)) = (-3, -0.5)

R''' = R'' + P =

P''' = P'' + P =

S''' = S'' + P =

Step 1, convert Q, R, P, and S to coordinates measured from point P rather than from the origin by subtracting P from each point:

Q' = Q-P = (-3-(-3),2-(-3)) = (0,5)

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

P' = P-P = (-3-(-3),-3-(-3)) =(0,0)

S' = S-P = (1-(-3),-3-(-3)) = (4,0)

Step 2, Apply the dilation factor (0.5):

Q'' = (0.5)Q' = (0.5*0, 0.5*5) = (0,2.5)

R'' = (0.5)R' =

P''= (0.5)P' =

S''= (0.5)S' =

Step 3, Convert coordinates back to the origin (vice point P) by adding P to each point.  These are the dilated points.

Q''' = Q'' + P = (0+(-3),2.5+(-3)) = (-3, -0.5)

R''' = R'' + P =

P''' = P'' + P =

S''' = S'' + P =

Step-by-step explanation: