Answer:
The scale factor of the dilation is 0.2 or \(\frac{1}{5}\).
Step-by-step explanation:
The vertices of pre-image are A(−3, 4), B(−1, 12), C(4, −2).
The vertices of image are A'(−0.6, 0.8), B'(−0.2, 2.4), C'(0.8, −0.4).
If scale factor of dilation is k and center of dilation is origin, then
\(P(x,y)\rightarrow P'(kx,ky)\)
It is given that A(−3, 4).
\(A(−3, 4)\rightarrow A'(k(-3),k(4))\)
Therefore the image of A is
A'(k(-3),k(4))
A'(-3k,4k) .... (1)
It is given that the image of A is
A'(−0.6, 0.8) .... (2)
On comparing (1) and (2), we get
\(-3k=-0.6\)
Divide both sides by -3.
\(k=\frac{-0.6}{-3}\)
\(k=0.2\)
If center of dilation is origin, then the direct formula to calculate scale factor is
\(k=\frac{\text{coordinate of x'}}{\text{coordinate of x}}\)
\(k=\frac{-0.6}{-3}\)
\(k=0.2\)
Therefore the scale factor of the dilation is 0.2 or \(\frac{1}{5}\).
