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.

Answer 1

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

\[
(x', y') = (k \cdot x, k \cdot y)
\]

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

Given:

- Point \( A(-6, 4) \)
- Point \( B(-8, 2) \)
- Scale factor \( k = 12 \)

Let's calculate the new coordinates:

1. For point \( A(-6, 4) \):

\[
A' = (12 \cdot -6, 12 \cdot 4) = (-72, 48)
\]

2. For point \( B(-8, 2) \):

\[
B' = (12 \cdot -8, 12 \cdot 2) = (-96, 24)
\]

Therefore, the coordinates after dilation are:

- \( A'(-72, 48) \)
- \( B'(-96, 24) \)