To find the coordinates of points A′ and B′ after a dilation with a scale factor of 5 centered at the origin, we can use the following formula for dilation:
\[ A' = (k \cdot x_A, k \cdot y_A) \]
\[ B' = (k \cdot x_B, k \cdot y_B) \]
where \( k \) is the scale factor, \( (x_A, y_A) \) are the coordinates of point A, and \( (x_B, y_B) \) are the coordinates of point B.
Given:
- Point A is at (1, 2)
- Point B is at (−2, −1)
- Scale factor \( k = 5 \)
Now we can calculate the coordinates of points A′ and B′.
For point A′: \[ A' = (5 \cdot 1, 5 \cdot 2) = (5, 10) \]
For point B′: \[ B' = (5 \cdot -2, 5 \cdot -1) = (-10, -5) \]
Thus, the coordinates of A′ and B′ after the dilation are:
- A′ (5, 10)
- B′ (−10, −5)
This corresponds to the second option in the provided responses: A′ (5, 10) and B′ (−10, −5).
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