Answer:
[tex]\dfrac12[/tex]
Step-by-step explanation:
The endpoints AB are at (0,-7) and (8,8)
The endpoints A'B' are at (6,-6) and (2,1.5)
To determine the scale factor of the dilation, we determine the lengths of the segments AB and A'B' using the distance formula.
[tex]AB=\sqrt{(8-0)^{2}+(8-(-7))^{2}}\\=\sqrt{8^{2}+15^{2}}\\=\sqrt{64+225}\\=\sqrt{289}\\AB=17[/tex]
[tex]A^{\prime} B^{\prime}=\sqrt{(2-6)^{2}+(1.5-(-6))^{2}}\\=\sqrt{4^{2}+7.5^{2}} \\=\sqrt{16+56.25}\\=\sqrt{72.25}\\A'B'=8.5[/tex]
Length of AB in the pre-image = 17 Units
Length of AB in the image, A'B'=8.5 Units
Therefore, the scale factor of the dilation
= [tex]\dfrac{8.5}{17}=\dfrac12[/tex]
