Question

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Consider this dilation.



(a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b) What is the scale factor? Explain and show your work.

ANSWER BOTH PARTS YOU MAY GET EXTRA POINTS!

Answer 1

• reduction
• scale factor 1/2

Explanation:

The usual English meanings of the words "reduction" and "enlargement" apply to geometrical figures.

(a)

Figure A'B'C'D' is smaller than figure ABCD, so represents a reduction.

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(b)

Every coordinate of every image point is half as far from the origin in A'B'C'D' as in the original figure ABCD. For example, the x-coordinate of C' is 2, and the x-coordinae of C is 4. The dilation factor is the ratio of these values:

k = Cx'/Cx = 2/4 = 1/2

The scale factor is 1/2.