Answer:
The scale factor of the dillation is -4.
Explanation:
We must remember that dilation of a given point [tex](x,y)[/tex] with respect to a point [tex](h,k)[/tex] is represented by the following operation:
[tex](x',y') = (h,k)+\alpha\cdot [(x,y)-(h,k)][/tex], [tex]\forall \,\alpha \in \mathbb{R}[/tex]
Where:
[tex]x'[/tex], [tex]y'[/tex] - Location of the dillated vertex.
[tex]\alpha[/tex] - Factor of dillation.
If we know that [tex](x,y) = (2,3)[/tex], [tex](h,k) = (0,0)[/tex] and [tex](x',y') = (-8,-12)[/tex], then, we solve the resulting expression:
[tex](-8,-12) = (0,0) +\alpha\cdot[ (2,3)-(0,0)][/tex]
[tex](-8,-12) = (0,0)+\alpha \cdot (2-0,3-0)[/tex]
[tex](-8,-12) = (0,0) + (2\cdot \alpha,3\cdot \alpha)[/tex]
[tex](-8,-12) = (2\cdot \alpha, 3\cdot \alpha)[/tex]
Whose solution is [tex]\alpha = -4[/tex].
The scale factor of the dillation is -4.
