Question

2. Quadrilateral ABCD was dilated with the origin as the center of dilation to create quadrilateral A'B'C'D. Which rule best represents the dilation that was applied to quadrilateral ABCD to create quadrilateral A'B'C'D ?

Answer 1

`(x,y) => (2.5x,2.5y)`

Explanation:

Given

See attachment for ABCD and A'B'C'D'

Required

Determine the dilation rule

Using AB and A'B' as points of references;

`AB = (-1,2)\ to\ (2,1)`

`A'B' = (-2.5,5)\ to\ (5,2.5)`

The dilation factor (k) is calculated as:

`k = (A'B')/(AB)`

This gives:

`k = ((-2.5,5))/((-1,2)) \ or\ k = ((5,2.5))/((2,1))`

Factorize

`k = (2.5*(-1,2))/((-1,2)) \ or\ k = (2.5*(2,1))/((2,1))`

`k = 2.5 \ or\ k = 2.5`

Hence, the scale factor is 2.5

The dilation rule is:

`(x,y) => k(x,y)`

`(x,y) => 2.5(x,y)`

`(x,y) => (2.5x,2.5y)`