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patriot [66]
3 years ago
5

Triangle ABC is transformed with the center of dilation at the origin. Pre-image: △ABC with vertices A(−3, 4), B(−1, 12), C(4, −

2) Image: △A'B'C' with vertices A'(−0.6, 0.8), B'(−0.2, 2.4), C'(0.8, −0.4) What is the scale factor of the dilation that maps the pre-image to the image?

Mathematics
2 answers:
Anestetic [448]3 years ago
6 0

Answer:

The scale factor of the dilation is 0.2 or \frac{1}{5}.

Step-by-step explanation:

The vertices of pre-image are A(−3, 4), B(−1, 12), C(4, −2).

The vertices of image are A'(−0.6, 0.8), B'(−0.2, 2.4), C'(0.8, −0.4).

If scale factor of dilation is k and center of dilation is origin, then

P(x,y)\rightarrow P'(kx,ky)

It is given that A(−3, 4).

A(−3, 4)\rightarrow A'(k(-3),k(4))

Therefore the image of A is

A'(k(-3),k(4))

A'(-3k,4k)             .... (1)

It is given that the image of A is

A'(−0.6, 0.8)       .... (2)

On comparing (1) and (2), we get

-3k=-0.6

Divide both sides by -3.

k=\frac{-0.6}{-3}

k=0.2

If center of dilation is origin, then the direct formula to calculate scale factor is

k=\frac{\text{coordinate of x'}}{\text{coordinate of x}}

k=\frac{-0.6}{-3}

k=0.2

Therefore the scale factor of the dilation is 0.2 or \frac{1}{5}.

Marysya12 [62]3 years ago
5 0
<span>When triangle ABC is transformed with the center of dilation at the origin. The image will  become △ABC with vertices A(−3, 4), B(−1, 12), C(4, −2). The scale factor of the dilation that maps the pre-image to the image is 8:3</span>
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