Dilation Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

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

Solution

  1. 1
    Step 1: Multiply each coordinate by k=2k = 2: A′(2,2)A'(2,2), B′(6,2)B'(6,2), C′(6,6)C'(6,6), D′(2,6)D'(2,6).
  2. 2
    Step 2: Original side length =2= 2. New side length =2×2=4= 2 \times 2 = 4. Verify: ∣Bx′−Ax′∣=∣6−2∣=4|B'_x - A'_x| = |6 - 2| = 4. ✓

Answer

A′(2,2)A'(2,2), B′(6,2)B'(6,2), C′(6,6)C'(6,6), D′(2,6)D'(2,6); new side length =4= 4.
Dilation with scale factor k=2k=2 doubles every distance from the origin, including side lengths. The figure remains a square — shape is preserved — but it is positioned twice as far from the origin and has sides twice as long.

About Dilation

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

Learn more about Dilation →

More Dilation Examples

Example 1 easy

Triangle [formula] has vertices [formula], [formula], [formula]. Apply a dilation from the origin wi

Example 2 medium

Point [formula] is dilated from the origin with scale factor [formula]. Find the image [formula] and

Example 4 hard

After a dilation from the origin, point [formula] maps to [formula]. Find the scale factor [formula]

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