Question

The smaller triangle is a pre-image of the bigger triangle the center dilation is (1,-1) What is the scale factor used to create the dilation?
A. 4
B. -4
C. 6
D. 1/4

Answer 1

Answer: The answer is B: -4

-4 Is your answer.

Answer 2

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):

$(1,-1),(1,1)$

Length of side:

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\sqrt{((1-1)^2+1-(-1))^2}=\sqrt{0+(1+1)^2} = \sqrt{4} =\pm2$

Since distance is always positive so its 2 units.

2 Vertices of bigger triangle(Image):

$(1,-1),(1,-9)$

Length of side:

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\sqrt{((1-1)^2+(-9-(-1))^2}=\sqrt{0+(-9+1)^2} = \sqrt{(-8)^2}= \sqrt{64} =\pm8$

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 = $-\frac{length\ of \ image}{length\ of\ pre-image} =-\frac{8}{2} = -4$

Scalar factor =-4