To find point \( Q \) such that \( \overline{DQ} \) is an enlargement of \( \overline{DF} \) by a scale factor of 2 with point \( D \) as the center of dilation, we first need the coordinates of points \( D \) and \( F \).
Let's assume that:
- The coordinates of point \( D \) are \( (x_D, y_D) \)
- The coordinates of point \( F \) are \( (x_F, y_F) \)
Given that the scale factor is 2, we can determine the coordinates of point \( Q \) using the formula for dilation:
\[ Q = D + 2( F - D ) \]
This can also be expressed as:
\[ Q = (1 - k) D + k F \]
where \( k \) is the scale factor (which is 2).
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Find point \( F \) given your graphical coordinate system (it looks like a grid), hence let's define \( D \) and \( F \).
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Calculate point \( Q \): If \( D \) has coordinates \( (x_D, y_D) \) and \( F \) has coordinates \( (x_F, y_F) \), then:
\[ Q = (x_D + 2(x_F - x_D), y_D + 2(y_F - y_D)) \]
This simplifies to:
\[ Q = (2x_F - x_D, 2y_F - y_D) \]
If I could have the specific coordinates for points \( D \) and \( F \), I can substitute them into the equation above to find the exact coordinates of point \( Q \).