Question

Triangle DEF is a dilation of Triangle ABC with center (0, 0). What is the scale factor?

Answer 1

Scale factor

The formula for the scale factor(k) with the origin is given by:

`(x, y) \rightarrow (kx, ky)`

In the given figure,

triangle DEF is a dilation of a triangle ABC with center (0, 0)

Coordinates of image DEF are;

`D = (-2, 1)`

`E= (0, 2)`

`F = (1, -1)`

Also, coordinate of pre-image ABC are:

`A = (-6, 3)`

`B= (0, 6)`

`C= (3, -3)`

Now, using dilation rule to solve for k;

`A(-6, 3) \rightarrow D(-6k, 3k)`

On comparing:

D(-6k, 3k) = D(-2, 1)

we get;

-6k = -2

Divide both sides by -6 we get;

`k = (1)/(3)`

Therefore, the scale factor(k) is,
`(1)/(3)`