Question

The coordinates of the vertices of triangle ABC are A(3,6), B(6, 3), and C(9, 9). If triangle ABC Is dilated by 1/3x and 1/3y to create triangle A'B'C', which set of coordinates represents the vertices of triangle ABC?

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Answer 1

`A' = (1,2)`

`B'=(2,1)`

`C' =(3,3)`

Explanation:

Given

`A = (3,6)`

`B = (6,3)`

`C = (9,9)`

`Scale = (1)/(3)`

Required

Determine the vertices of ABC

If truly the question asks for the vertices of ABC, then the vertices are:

`A = (3,6)`
`B = (6,3)`
`C = (9,9)`

However, I'm quite sure that's not the requirement of the question. So, I'll solve for A'B'C'

To do this, we simply multiply the vertices of ABC by the scale of dilation.

`(A'B'C') = Scale\ Factor * (ABC)`

`A' = (1)/(3) * A`

`A' = (1)/(3) * (3,6)`

`A' = ((3)/(3),(6)/(3))`

`A' = (1,2)`

`B' = (1)/(3) * B`

`B' = (1)/(3) * (6,3)`

`B' = ((6)/(3),(3)/(3))`

`B'=(2,1)`

`C' = (1)/(3) * C`

`C' = (1)/(3) * (9,9)`

`C' = ((9)/(3),(9)/(3))`

`C' =(3,3)`