Question

What is the image of(8,12) after a dilation by a scale factor of 1/4 centered at the origin?

Answer 1

Answer:  (2, 3)

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Explanation:

1/4 = 0.25 is the scale factor

Multiply this with each coordinate of the given point

0.25*8 = 2 is the new x coordinate

0.25*12 = 3 is the new y coordinate

So (8,12) moves to (2,3) after applying the dilation

The scale factor k makes 0 < k < 1 true, so the point is closer to the origin after applying the dilation.

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Side note: this trick of multiplying the scale factor by each coordinate only works if the dilation is centered at the origin. For any other center, you'll need to apply a translation first, dilate, then translate back again.