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, \(\frac{1}{3}\)
