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 the points \( A' \) and \( B' \) after a dilation with a scale factor of 12 centered at the origin, we can use the formula for dilation. If a point \( (x, y) \) is dilated with a scale factor \( k \), the new coordinates \( (x', y') \) are given by:

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

Here, \( k = 12 \).

### Step 1: Find \( A' \)

The coordinates of point \( A \) are \( (-6, 4) \).

Using the dilation formula:

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

### Step 2: Find \( B' \)

The coordinates of point \( B \) are \( (-8, 2) \).

Using the dilation formula:

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

### Conclusion

The coordinates of the dilated points are:

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