Segment Y prime Z prime has endpoints located at Y'(0, 3) and Z'(−6, 3). segment YZ was dilated at a scale factor of 3 from the origin. Which statement describes the pre-image? segment YZ is located at Y (0, 9) and Z (−18, 9) and is three times the size of segment Y prime Z prime.
segment YZ is located at Y (0, 3) and Z (−6, 3) and is the same size as segment Y prime Z prime.
segment YZ is located at Y (0, 1.5) and Z (−3, 1.5) and is the one-half the size of segment Y prime Z prime.
segment YZ is located at Y (0, 1) and Z (−2, 1) and is one-third the size of segment Y prime Z prime.

the only one that makes sense is The last one D

Step-by-step explanation:

1 is 1/3 of 3 and -2,1 is 1/3 of -6,3

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!