Answer:
Scale factor
The formula for the scale factor(k) with the origin is given by:
[tex](x, y) \rightarrow (kx, ky)[/tex]
In the given figure,
triangle DEF is a dilation of a triangle ABC with center (0, 0)
Coordinates of image DEF are;
[tex]D = (-2, 1)[/tex]
[tex]E= (0, 2)[/tex]
[tex]F = (1, -1)[/tex]
Also, coordinate of pre-image ABC are:
[tex]A = (-6, 3)[/tex]
[tex]B= (0, 6)[/tex]
[tex]C= (3, -3)[/tex]
Now, using dilation rule to solve for k;
[tex]A(-6, 3) \rightarrow D(-6k, 3k)[/tex]
On comparing:
D(-6k, 3k) = D(-2, 1)
we get;
-6k = -2
Divide both sides by -6 we get;
[tex]k = \frac{1}{3}[/tex]
Therefore, the scale factor(k) is, [tex]\frac{1}{3}[/tex]
