Question

y
10-
9
-8
7
6-
F
5-
4
3
D
2-
x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
t-1+
-2-
-3-
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 =

Answer 1

To find point \( Q \) such that \( \overline{DQ} \) is an enlargement of \( \overline{DF} \) by a scale factor of 2 with point \( D \) as the center of dilation, we first need the coordinates of points \( D \) and \( F \).

Let's assume that:
- The coordinates of point \( D \) are \( (x_D, y_D) \)
- The coordinates of point \( F \) are \( (x_F, y_F) \)

Given that the scale factor is 2, we can determine the coordinates of point \( Q \) using the formula for dilation:

\[
Q = D + 2( F - D )
\]

This can also be expressed as:

\[
Q = (1 - k) D + k F
\]

where \( k \) is the scale factor (which is 2).

1. **Find point \( F \)** given your graphical coordinate system (it looks like a grid), hence let's define \( D \) and \( F \).

2. **Calculate point \( Q \)**:
If \( D \) has coordinates \( (x_D, y_D) \) and \( F \) has coordinates \( (x_F, y_F) \), then:

\[
Q = (x_D + 2(x_F - x_D), y_D + 2(y_F - y_D))
\]

This simplifies to:

\[
Q = (2x_F - x_D, 2y_F - y_D)
\]

If I could have the specific coordinates for points \( D \) and \( F \), I can substitute them into the equation above to find the exact coordinates of point \( Q \).