Answer:
B. -4
Step-by-step explanation:
When dilation is not about the origin then in order to find the scalar factor, we need to find the ratio of the corresponding lengths.
2 Vertices of smaller triangle (Pre-image):
[tex](1,-1),(1,1)[/tex]
Length of side:
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{((1-1)^2+1-(-1))^2}=\sqrt{0+(1+1)^2} = \sqrt{4} =\pm2[/tex]
Since distance is always positive so its 2 units.
2 Vertices of bigger triangle(Image):
[tex](1,-1),(1,-9)[/tex]
Length of side:
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{((1-1)^2+(-9-(-1))^2}=\sqrt{0+(-9+1)^2} = \sqrt{(-8)^2}= \sqrt{64} =\pm8[/tex]
Since distance is always positive so its 8 units.
For the given figure we see that the dilated image is rotated 180° from the original position. Thus, for such dilation the scalar factor is taken negative.
Thus the scalar factor can be calculated as:
Scalar factor = [tex]-\frac{length\ of \ image}{length\ of\ pre-image} =-\frac{8}{2} = -4[/tex]
Scalar factor =-4
