Question

D (3,2)
F (8,4)

Find point H to prove that DH is enlargement of DF by a scale factor of 2 with point D as the center of dilation

a. H is at (13,6)
b. H is at (5.5,3)
c. H is at (-2,0)
d. H is at (8,18)

Answer 1

To find point H such that DH is an enlargement of DF by a scale factor of 2 with point D as the center of dilation, we can use the formula for dilation:

\[
H = D + k \cdot (F - D)
\]

where:
- \(k\) is the scale factor (in this case, 2)
- \(D\) is the original point
- \(F\) is the point we are dilating from

Given:
- \(D = (3, 2)\)
- \(F = (8, 4)\)

First, we need to calculate \(F - D\):

\[
F - D = (8 - 3, 4 - 2) = (5, 2)
\]

Now, we apply the scale factor:

\[
H = D + 2 \cdot (F - D) = (3, 2) + 2 \cdot (5, 2) = (3, 2) + (10, 4) = (3 + 10, 2 + 4) = (13, 6)
\]

Now we can check which of the provided options corresponds to the coordinates we calculated for H:

a. \(H\) is at \( (13,6) \) (Correct)
b. \(H\) is at \( (5.5,3) \)
c. \(H\) is at \( (-2,0) \)
d. \(H\) is at \( (8,18) \)

So, the correct answer is:

**a. H is at (13,6)**.