Mathematics, 15.11.2019 23:31 ariannapenny98

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

The smaller triangle is a pre-image of the bigger triangle the center dilation is (1,-1) what is the

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Answer from: ethanw7327

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

Answer from: Quest

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Answer from: Quest

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The smaller triangle is a pre-image of the bigger triangle the center dilation is (1,-1) what is the...