Question

If center of dilation is D (-1, -1) and the coordinates for triangle ABC are A(0, -2), B(2, -4), and C(3, -1), then what are the coordinates of triangle A'B'C' after a dilation with a scale factor of 2?

Answer 1

A'(1,-3), B'(7,-1) and C'(5,-7).

Explanation:

Given,

The coordinates of the triangle ABC are,

A(0, -2), B(2, -4), and C(3, -1)

If a point (x,y) is dilated about a point (p,q) with a scale factor k,

Then the dilation rule is,

`(x,y)\rightarrow (k(x-p)+p, k(y-q)+q)`

Here, the triangle ABC with coordinates A(0, -2), B(2, -4), and C(3, -1) is dilated with scale factor 2 about a point (-1,-1) to form triangle A'B'C'.

That is, k = 2, p = -1, q = -1

Then,

`(0,-2)\rightarrow (2(0+1)-1,2(-2+1)-1)=(1,-3)`

Similarly,

`(2,-4)\rightarrow (5,-7)`

`(3,-1)\rightarrow (7,-1)`

Therefore, the coordinates of triangle A'B'C' are,

A'(1,-3), B'(5,-7) and C'(7,-1)