Question

Under a dilation of scale factor 3/2 centered at (3, 7), point R(1, 1) becomes R' and point T(5, 5) becomes T'. Determine the coordinates of R' and T'.

A) R'(2, 2) T'(5, 5)
B) R'(1.5, 1.5) T'(3.75, 3.75)
C) R'(4.5, 4.5) T'(7.5, 7.5)
D) R'(4, 4) T'(6, 6)

Answer 1

Upon applying the dilation formula to points R(1, 1) and T(5, 5), it appears that we might have made a mistake, as the coordinates for R' do not match any of the options provided. Without a correct answer, we cannot supply the answer choices given.

Step-by-step explanation:

To perform a dilation of points R(1, 1) and T(5, 5) with a scale factor of 3/2, centered at (3, 7), we apply the dilation formula:

R'(x, y) = [(x - x_center) × scale_factor + x_center, (y - y_center) × scale_factor + y_center]

For point R(1, 1):

R' = [(1 - 3) × 3/2 + 3, (1 - 7) × 3/2 + 7]

R' = [(-2) × 3/2 + 3, (-6) × 3/2 + 7]

R' = [-3 + 3, -9 + 7]

R' = [0, -2]

This is not matching with any of the options given, so let's also check T(5, 5).

For point T(5, 5):

T' = [(5 - 3) × 3/2 + 3, (5 - 7) × 3/2 + 7]

T' = [2 × 3/2 + 3, -2 × 3/2 + 7]

T' = [3 + 3, -3 + 7]

T' = [6, 4]

Since the coordinates of R' do not match any of the options provided and we might have made a mistake, we cannot confidently provide a correct answer for the choices given.