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What is the scale factor applied when triangle DEH is dilated to make triangle DFG?

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The figure shows two semicircles centered at G and H. Point B is on both semicircles. Line DF touches each circle at one point only, points F and E. If DE = 4 and EF = 8, what is the scale factor applied when triangle DEH is dilated to make triangle DFG?

1/2
1/3
2
3




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    1 Answer

    1. Quizzma Team

      To find the scale factor when triangle DEH is dilated to become triangle DFG, we need to examine the triangles formed by the segments DE, EF, and the lengths between points D, E, and F.

      Given that DE = 4 and EF = 8, the total length of DF is:

      DF = DE + EF = 4 + 8 = 12.

      Now, if we are comparing the lengths of corresponding sides in the two triangles, we can examine the ratio of the sides.

      The corresponding side for DE in triangle DFG would be DF, which is 12.

      To find the scale factor (k), we set up the ratio:

      k = length of DE / length of DF = 4 / 12 = 1/3.

      Thus, the scale factor applied when triangle DEH is dilated to make triangle DFG is 1/3.

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