Question

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

Answer 1

Hi their! The correct answer your looking for is:

1/3

Hope this helps, and have a great day!

Answer 2

Answer:

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;

$k = \frac{1}{3}$

Therefore, the scale factor(k) is, $\frac{1}{3}$