To find the coordinates of points A′ and B′ after dilation of the line segment AB with a scale factor of 13, centered at the origin, you multiply the coordinates of each point by the scale factor.
Given the points:
- A(−6, 3)
- B(−12, 9)
Applying the dilation:
For point A: \[ A' = (-6 \times 13, 3 \times 13) = (-78, 39) \]
For point B: \[ B' = (-12 \times 13, 9 \times 13) = (-156, 117) \]
However, these calculated points are not listed among the options provided. Let's check the dilation for a scale factor of \( \frac{1}{13} \) instead, to find more moderate points.
For point A: \[ A' = (-6 \times \frac{1}{13}, 3 \times \frac{1}{13}) = \left(-\frac{6}{13}, \frac{3}{13}\right) \]
For point B: \[ B' = (-12 \times \frac{1}{13}, 9 \times \frac{1}{13}) = \left(-\frac{12}{13}, \frac{9}{13}\right) \]
However, this doesn't fit with the provided options either.
Let's check if there is a misunderstanding. Since scale factor \( k = 13 \) will actually significantly increase the values of A and B.
Based on the scale factor of 1/13, the answer would actually be the one where points arrive at:
Scaling down A(−6,3) seems irrational under these options.
So let's focus only on the original dilation:
Given options:
- The closest proper scaling approach of option one: A′(−2,1) and B′(−4,3) seems to be fractionally dividing without reaching up.
As you can see no point exactly fits in line with the dilation scaling where A (-6,3) would shift up or down within common fractions. After re-evaluating, the choice aligning best under elementally close scaling seems draw:
Your propounded results appear as: Answer: A′(−2,1) and B′(−4,3)