What is the scale factor in the dilation if the coordinates of A prime are (–7, 6) and the coordinates of C prime are (–4, 3)? On a coordinate plane, square A B C D has points (negative 21, 18), (negative 12, 18), (negative 12, 9), (negative 21, 9). Square A prime B prime C prime D prime has points (negative 8, 6), (negative 4, 6), (negative 4, 3), (negative 8, 3). One-third One-half 2 3

The scale factor of dilation is One-third

Step-by-step explanation:

If point (x , y) is dilated by a scale factor k, then its image is (kx , ky)

∵ The vertices of the square ABCD are:

A = (-21 , 18)

B = (-12 , 18)

C = (-12 , 9)

D = (-21 , 9)

∵ A' = (-7 , 6)

∴ (kx , ky) = (-7 , 6)

∵ x , y are the coordinates of Point A

∵ x = -21 and kx = -7

∴ k(-21) = - 7

- Divide both sides by -21

∴ k =

∵ y = 18 and ky = 6

∴ k(18) = 6

- Divide both sides by 18

∴ k =

∵ C' = (-4 , 3)

∴ (kx , ky) = (-4 , 3)

∵ x , y are the coordinates of Point C

∵ x = -12 and kx = - 4

∴ k(-12) = - 4

- Divide both sides by -12

∴ k =

∵ y = 9 and ky = 3

∴ k(9) = 3

- Divide both sides by 9

∴ k =

∴ The scale factor of dilation is One-third

hi

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