Question

Dilations Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
Line segment AB
has endpoints A (−6, 4)
and B (−8, 2)
. Find the coordinates of A′
and B′
after a dilation with a scale factor of 12
, centered at the origin.(1 point)
A′
(
) B′
(
)
Remaining Attempts : 2

Answer 1

To find the coordinates of \( A' \) and \( B' \) after a dilation centered at the origin with a scale factor of 12, we can use the following formula for dilation:

\[
(x', y') = (kx, ky)
\]

where \( (x, y) \) are the original coordinates, \( k \) is the scale factor, and \( (x', y') \) are the new coordinates after dilation.

### For point A (-6, 4):
- Scale factor \( k = 12 \)
- Original coordinates \( (x, y) = (-6, 4) \)

Calculating \( A' \):
\[
A' = (12 \times -6, 12 \times 4) = (-72, 48)
\]

### For point B (-8, 2):
- Scale factor \( k = 12 \)
- Original coordinates \( (x, y) = (-8, 2) \)

Calculating \( B' \):
\[
B' = (12 \times -8, 12 \times 2) = (-96, 24)
\]

### Final Answer:
- \( A' (-72, 48) \)
- \( B' (-96, 24) \)