To find the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 13, centered at the origin, we will apply the dilation formula for each endpoint.
The formula for dilation centered at the origin with a scale factor \( k \) is given by: \[ (x', y') = (kx, ky) \]
Original Endpoints
The original endpoints are:
- \( A(-6, 3) \)
- \( B(-12, 9) \)
Dilation by a Scale Factor of 13
-
For point A: \[ A' = (13 \cdot -6, 13 \cdot 3) = (-78, 39) \]
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For point B: \[ B' = (13 \cdot -12, 13 \cdot 9) = (-156, 117) \]
Result
The coordinates after dilation are:
- \( A'(-78, 39) \)
- \( B'(-156, 117) \)
So the original endpoints are \( A(-6, 3) \) and \( B(-12, 9) \), and the dilated endpoints are \( A'(-78, 39) \) and \( B'(-156, 117) \).