To find the coordinates of the points A' and B' after dilating the line segment AB with a scale factor of 13, centered at the origin, you can use the formula for dilation:
\[ (x', y') = (kx, ky) \]
where \((x, y)\) are the original coordinates of the point, \(k\) is the scale factor, and \((x', y')\) are the coordinates after dilation.
Given:
- Point A is \((-6, 3)\) and point B is \((-12, 9)\).
- The scale factor \(k = 13\).
Now, let's calculate the coordinates A' and B' for both points.
- For point A \((-6, 3)\):
\[ A' = (13 \cdot -6, 13 \cdot 3) = (-78, 39) \]
- For point B \((-12, 9)\):
\[ B' = (13 \cdot -12, 13 \cdot 9) = (-156, 117) \]
Thus, after the dilation, the coordinates of points A' and B' are:
- \(A' = (-78, 39)\)
- \(B' = (-156, 117)\)
These are the new coordinates after applying a dilation with a scale factor of 13 centered at the origin.