Practice Dilation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A transformation that enlarges or shrinks a figure by a scale factor from a center point.

Like zooming in or out on a photo—everything gets bigger or smaller proportionally.

Example 1

easy
Triangle ABC has vertices A(2, 4), B(6, 0), C(4, 8). Apply a dilation from the origin with scale factor k = 3. Find the image vertices A', B', C'.

Example 2

medium
Point P(8, 12) is dilated from the origin with scale factor k = \dfrac{1}{4}. Find the image P' and compare the distance from the origin to P' vs. to P.

Example 3

easy
Square ABCD has vertices A(1,1), B(3,1), C(3,3), D(1,3). After a dilation from the origin with scale factor k = 2, find the new vertices and the new side length.

Example 4

hard
After a dilation from the origin, point Q(3, 5) maps to Q'(7.5, 12.5). Find the scale factor k. Then determine by what factor the area of any figure changes under this dilation.
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