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
do they get smaller

Answer 1

To perform a dilation centered at the origin with a scale factor of \( k = 12 \), we multiply the coordinates of each endpoint of the line segment by the scale factor.

The original coordinates of points A and B are:
- \( A (-6, 4) \)
- \( B (-8, 2) \)

Now we apply the scale factor of 12 to each coordinate:

**For point A:**
\[
A' = (k \cdot x_A, k \cdot y_A) = (12 \cdot -6, 12 \cdot 4) = (-72, 48)
\]

**For point B:**
\[
B' = (k \cdot x_B, k \cdot y_B) = (12 \cdot -8, 12 \cdot 2) = (-96, 24)
\]

So, after the dilation with a scale factor of 12, the coordinates of the points are:
- \( A' (-72, 48) \)
- \( B' (-96, 24) \)

These coordinates are indeed larger in absolute value compared to the original coordinates of A and B. Therefore, the points do not get smaller; they get larger as a result of the dilation.