Problem 131 of 7
Complete a proof that dilation scales segments: Let segment AB have endpoints A(x1, y1) and B(x2, y2). After dilation centered at the origin with scale factor k, the image points are A'(kx1, ky1) and B'(kx2, ky2).
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Hidden until you reveal it.
use coordinates, vectors, or similarity.
Hidden until you reveal it.
Completion must use coordinates, vectors, or similarity to justify length scaling.
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Your answer is equivalent to the expected form.
Walkthrough
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1. Express original and image segment in coordinates, vectors, or similar triangles.
2. Show each linear component scales by k.
3. Conclude the segment length scales by k.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Only stating the formula without justification.