Question
Find point H to prove that line DH is an enlargement of line DF by a scale factor of 2 with point D as the center of dilation
Coordinate D is at (3,2)
Coordinate F is at ( 8,4)
Coordinate D is at (3,2)
Coordinate F is at ( 8,4)
Answers
GPT-4o mini
To find point H such that line DH is an enlargement of line DF by a scale factor of 2 with point D as the center of dilation, we can follow these steps:
1. **Determine the vector from D to F**:
The coordinates of D are (3, 2) and F are (8, 4). The vector DF can be calculated as:
\[
DF = (F_x - D_x, F_y - D_y) = (8 - 3, 4 - 2) = (5, 2)
\]
2. **Scale this vector by the scale factor**:
Since the scale factor is 2, we will scale the vector DF by multiplying it by 2:
\[
\text{Scaled vector} = (2 \times 5, 2 \times 2) = (10, 4)
\]
3. **Calculate the coordinates of point H**:
We can find point H by adding the scaled vector to point D:
\[
H = (D_x + \text{Scaled vector}_x, D_y + \text{Scaled vector}_y) = (3 + 10, 2 + 4) = (13, 6)
\]
Thus, the coordinates of point H are \((13, 6)\).
To summarize, point H is at \((13, 6)\), making line DH an enlargement of line DF by a scale factor of 2, with point D as the center of dilation.
1. **Determine the vector from D to F**:
The coordinates of D are (3, 2) and F are (8, 4). The vector DF can be calculated as:
\[
DF = (F_x - D_x, F_y - D_y) = (8 - 3, 4 - 2) = (5, 2)
\]
2. **Scale this vector by the scale factor**:
Since the scale factor is 2, we will scale the vector DF by multiplying it by 2:
\[
\text{Scaled vector} = (2 \times 5, 2 \times 2) = (10, 4)
\]
3. **Calculate the coordinates of point H**:
We can find point H by adding the scaled vector to point D:
\[
H = (D_x + \text{Scaled vector}_x, D_y + \text{Scaled vector}_y) = (3 + 10, 2 + 4) = (13, 6)
\]
Thus, the coordinates of point H are \((13, 6)\).
To summarize, point H is at \((13, 6)\), making line DH an enlargement of line DF by a scale factor of 2, with point D as the center of dilation.