Question

In the diagram, the circle will be dilated by a scale factor of 3 about the origin. The points C, A, and B map to C', A', and B' after the dilation. What is the length of ? Use the distance formula to help you decide: . The graph shows a circle with three points, A is equal to (8, 15), B is equal to (12, 13), and C is equal to (8, 10). C is the center of the circle. A line is joining AC and BC A. 24 units B. 45 units C. 21 units D. 15 units E. 5 units Reset Next

Answer 1

The length of C'B' after dilation using a scale factor of 3 is: D. 15 units.

What is Dilation?

Dilation is the reduction or enlargement of an image by a scale factor, whereby the original and new images are similar.

Applying the distance formula, we have:

BC = √[(8−12)² + (10−13)²]

BC = √(−4)² + (−3)²]

BC = √(16+9)

BC = √25

BC = 5 units

Applying the scale factor:

Length of C'B' = 3(5) = 15 units.

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