Question

y
10-
9
8
7
6
5-
F
432
4
..
D
2
-0+
TO
=3 -2
NI
3
4 5 6 7 8
10 11 12 13 14 15 16
-2-
-3-
Find point H
to prove that DH¯¯¯¯¯¯¯¯¯
is an enlargement of DF¯¯¯¯¯¯¯¯
by a scale factor of 2 with point D
as the center of dilation.

(1 point)
Responses

H
is at (13,6)
.
upper H is at left parenthesis 13 comma 6 right parenthesis .

H
is at (5.5,3)
.
upper H is at left parenthesis 5.5 comma 3 right parenthesis .

H
is at (8,18)
.
upper H is at left parenthesis 8 comma 18 right parenthesis .

H
is at (−2,0)
.

Answer 1

To find the point \( H \) such that line segment \( DH \) is an enlargement of line segment \( DF \) by a scale factor of 2 with point \( D \) as the center of dilation, we first need the coordinates of points \( D \) and \( F \).

Assuming you have the coordinates for point \( D \) and point \( F \), you would use the following steps:

1. **Determine Coordinates**: Let's say point \( D \) is at \((x_D, y_D)\) and point \( F \) is at \((x_F, y_F)\).

2. **Calculate the Vector DF**: This is found by subtracting coordinates:
\[
DF_x = x_F - x_D
\]
\[
DF_y = y_F - y_D
\]

3. **Apply the Scale Factor**: Since \( H \) is an enlargement of \( F \) with a scale factor of 2, we will multiply the vector by 2:
\[
DH_x = 2 \cdot DF_x = 2(x_F - x_D)
\]
\[
DH_y = 2 \cdot DF_y = 2(y_F - y_D)
\]

4. **Find Coordinates for H**: Now we add the enlarged vector to point \( D \):
\[
x_H = x_D + DH_x
\]
\[
y_H = y_D + DH_y
\]

After calculating the coordinates of point \( H \) with the information above, you can compare the results to the given options.

If we need specific numbers, please provide the coordinates of points \( D \) and \( F \) for exact calculations!