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Question


Find point Q to prove that DQ¯¯¯¯¯¯¯¯
is an enlargement of DF¯¯¯¯¯¯¯¯
by a scale factor of 2 with a point D as the center of dilation.

(1 point)
Q (
,
)
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Answer 1

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

1. **Identify the Coordinates of D and F**: You will need the coordinates of points D and F. Let's assume:
- \( D(x_D, y_D) \)
- \( F(x_F, y_F) \)

2. **Calculate the Vector DF**: This vector can be found using:
\[
DF = (x_F - x_D, y_F - y_D)
\]

3. **Enlargement by Scale Factor**: To enlarge the vector \( DF \) by a scale factor of 2, you multiply the vector by 2:
\[
DQ = 2 \cdot DF = 2 \cdot (x_F - x_D, y_F - y_D) = (2(x_F - x_D), 2(y_F - y_D))
\]

4. **Find the Coordinates of Q**: You can find the coordinates of Q by adding the vector \( DQ \) to the coordinates of D:
\[
Q = D + DQ = (x_D + 2(x_F - x_D), y_D + 2(y_F - y_D))
\]

5. **Final Result**: Substitute \( x_D, y_D, x_F, y_F \) into the formula to get the coordinates of Q.

For instance, if you assume \( D(1, 2) \) and \( F(3, 4) \):
- DF would be \( (3 - 1, 4 - 2) = (2, 2) \)
- Enlarged \( DQ \) would be \( (2 \cdot 2, 2 \cdot 2) = (4, 4) \)
- So, \( Q \) would be \( (1 + 4, 2 + 4) = (5, 6) \)

Thus, in this example, Q is \( (5, 6) \).

You need to replace the actual values of D and F to find the specific coordinates of Q.