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Triangle ABC has vertices A(5, 3) , B(3, 7) , and C(1, 4) . Triangle ABC is dilated, and the vertices of the image are A′(1.25, 0.75) , B′(0.75, 1.75) , and C′(0.25, 1) . The center of dilation is the origin. What is the scale factor of the dilation? A. 0.25 B. 0.5 C. 2 D. 4

Respuesta :

Let's compare the two points A(5,3) and A'(1.25, 0.75)

The x coordinates of the two points are 5 and 1.25 respectively

Let k be the scale factor. We multiply the scale factor k by the x coordinate of the original point to get the x coordinate of the new point
5*k = 1.25
k = 1.25/5
k = 0.25

The scale factor is 0.25; the answer is choice A

The linear dimensions are 1/4th of the original (or 25% of the original)

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