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 centered at the origin with a scale factor of \( k = 12 \), we can use the formula for dilation:

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

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

1. Apply the scale factor: \[ A' = (12 \cdot -6, 12 \cdot 4) = (-72, 48) \]

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

1. Apply the scale factor: \[ B' = (12 \cdot -8, 12 \cdot 2) = (-96, 24) \]

Thus, the coordinates after the dilation are:

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