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# Triangle ABC ​is transformed with the center of dilation at the origin.

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Triangle ABC ​is transformed with the center of dilation at the origin.

Pre-image: △ABC with vertices  A(2, 5), B(6, 10), C(9, −1)

Image: △A′B′C′ with vertices  A′(0.5, 1.25), B′(1.5, 2.5), C′(2.25, −0.25)

What is the scale factor of the dilation that maps the pre-image to the image?

AngelRay  Nov 14, 2017
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Do get the coordinates of the new image from the previous, divide the points of the original by the corresponding points, after translating them both so that the point of dilation is 0 (found by drawing lines through each corresponding point and seeing where they all intersect). In this case, A'B'C' has a relative scale factor of $$\frac{1}{4}$$.

helperid1839321  Nov 14, 2017