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

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl