To find point Q that proves \( DQ \) is an enlargement of triangle \( D(3,2) \) and \( F(8,4) \) by a scale factor of 2 with point D as the center of dilation, we can use the formula for dilation.
The formula for dilation from point \( D \) with scale factor \( k \) is given by:
\[ Q = D + k(F - D) \]
where \( D \) is the center of dilation, \( F \) is the original point, and \( k \) is the scale factor.
In this case, we have:
- \( D = (3, 2) \)
- \( F = (8, 4) \)
- \( k = 2 \)
Now we can find \( Q \) using the formula:
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Calculate \( F - D \): \[ F - D = (8 - 3, 4 - 2) = (5, 2) \]
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Scale \( F - D \) by the scale factor \( k = 2 \): \[ k(F - D) = 2(5, 2) = (10, 4) \]
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Add this result to point \( D \): \[ Q = D + k(F - D) = (3, 2) + (10, 4) = (3 + 10, 2 + 4) = (13, 6) \]
Therefore, point \( Q \) is:
\[ Q(13, 6) \]
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