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.
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