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?

The scale factor of the dilation is 0.2 or .

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

It is given that A(−3, 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

Divide both sides by -3.

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

Therefore the scale factor of the dilation is 0.2 or .

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step-by-step explanation:

answer: 10 meter

step-by-step explanation:

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