y

Question

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!