Answer: The value of the scale factor is [tex]-\frac{1}{2}[/tex].
Explanation:
It is given that the △E′F′G′ is the image of △EFG under a dilation through point C.
We know that the length of sides of image are in the proportion of length of sides of preimage. That proportion factor is also known as scale factor.
It is given that the length of FG is 8 cm and the length of F'G' is 4 cm.
[tex]k=\frac{F'G'}{FG} =\frac{4}{8} =\frac{1}{2}[/tex]
Therefore the side of image and preimage are in proportion of [tex]\frac{1}{2}[/tex].
Since the image and preimage are not on the same side of the center of dilation it means the factor must be negative. So,
[tex]k=-\frac{1}{2}[/tex].
Therefore, [tex]-\frac{1}{2}[/tex] is the scale factor of dilation.
