Question

Find point Q to prove that DQ¯¯¯¯¯¯¯¯ is an enlargement of DF¯¯¯¯¯¯¯¯ D is at (3,2) and F is at (8,4) by a scale factor of 2 with a point D as the center of dilation. (1 point)

Answer 1

To find the point \( Q \) such that the line segment \( \overline{DQ} \) is an enlargement of \( \overline{DF} \) by a scale factor of 2 with \( D \) as the center of dilation, we follow these steps:

1. **Identify the coordinates**:
- Point \( D \) is at \( (3, 2) \).
- Point \( F \) is at \( (8, 4) \).

2. **Calculate the vector \( DF \)**:
\[
DF = F - D = (8 - 3, 4 - 2) = (5, 2)
\]

3. **Scale the vector \( DF \) by the factor of 2**:
\[
DQ = 2 \times DF = 2 \times (5, 2) = (10, 4)
\]

4. **Find the coordinates of point \( Q \)** by adding the scaled vector \( DQ \) to point \( D \):
\[
Q = D + DQ = (3, 2) + (10, 4) = (3 + 10, 2 + 4) = (13, 6)
\]

Thus, the point \( Q \) is \( (13, 6) \).

### Conclusion:
To prove that \( \overline{DQ} \) is an enlargement of \( \overline{DF} \) by a scale factor of 2, your final answer for point \( Q \) is:
\[
\boxed{(13, 6)}
\]