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Triangle D has been dilated to create triangle D′. Use the image to answer the question.

image of a triangle labeled D with side lengths of 6, 8, 10 and a second triangle labeled D prime with side lengths of 18, 24, 30

Determine the scale factor used.
one half
2
3
one third

1 answer

To determine the scale factor used in the dilation from triangle D to triangle D′, you can compare the corresponding side lengths of the two triangles.

For triangle D, the side lengths are:

  • 6
  • 8
  • 10

For triangle D′, the side lengths are:

  • 18
  • 24
  • 30

To find the scale factor, you can divide the side lengths of triangle D′ by the corresponding side lengths of triangle D:

  1. For the side lengths 6 and 18: \[ \text{Scale factor} = \frac{18}{6} = 3 \]

  2. For the side lengths 8 and 24: \[ \text{Scale factor} = \frac{24}{8} = 3 \]

  3. For the side lengths 10 and 30: \[ \text{Scale factor} = \frac{30}{10} = 3 \]

Since the scale factor is consistent across all corresponding side lengths, the scale factor used is 3.