Question

Which of the following dilations was applied to ABCD to create AB’C’D’?

Answer 1

The answer is B

Explanation:

The dilation is 2/3. You can find that by comparing the sizes of the two shapes. Its being reducted in this case. Using the guide new/original you can put 2/3. Both spaes connect at coordinate (1,7).

(I also did this question in math nation)

Answer 2

B

Explanation:

Quadrilateral ABCD has its vertices at points A(1,7), B(4,6), C(6,1) and D(1,4).

Consider dilation centered at point A(1,7) with a scale factor
`(2)/(3).` This dilation has the rule

`(x,y)\rightarrow \left((2)/(3)x+(1)/(3),(2)/(3)y+(7)/(3)\right)`

Thus,

• 
  `A(1,7)\rightarrow A'(1,7)\ \left[(2)/(3)\cdot 1+(1)/(3)=1,\ (2)/(3)\cdot 7+(7)/(3)=7\right];`
• 
  `B(4,6)\rightarrow B'\left(3,6(1)/(3)\right)\ \left[(2)/(3)\cdot 4+(1)/(3)=3,\ (2)/(3)\cdot 6+(7)/(3)=(19)/(3)=6(1)/(3)\right];`
• 
  `C(6,1)\rightarrow C'\left(4(1)/(3),3\right)\ \left[(2)/(3)\cdot 6+(1)/(3)=(13)/(3)=4(1)/(3),\ (2)/(3)\cdot 1+(7)/(3)=3\right];`
• 
  `D(1,4)\rightarrow D'(1,5)\ \left[(2)/(3)\cdot 1+(1)/(3)=1,\ (2)/(3)\cdot 4+(7)/(3)=5\right];`

These are exactly coordinates of quadrilateral A'B'C'D'