Line AB contains point A(1, 2) and point B (−2, −1) . Find the coordinates of A′ and B′ after a dilation with a scale factor of 5 with a center point of dilation at the origin.
1.A′ (5, 10) and B′ (10, 5)
2.A′ (5, 10) and B′ (−2, −1)
3.A′ (1, 2) and B′ (−10, −5)
4.A′ (5, 10) and B′ (−10, −5)
To find the coordinates of A' and B' after a dilation with a scale factor of 5 with a center point of dilation at the origin, we will multiply the x and y coordinates of A and B by the scale factor.
For point A(1, 2):
The x-coordinate of A' = x-coordinate of A * scale factor = 1 * 5 = 5
The y-coordinate of A' = y-coordinate of A * scale factor = 2 * 5 = 10
Therefore, A' has coordinates (5, 10).
For point B(-2, -1):
The x-coordinate of B' = x-coordinate of B * scale factor = -2 * 5 = -10
The y-coordinate of B' = y-coordinate of B * scale factor = -1 * 5 = -5
Therefore, B' has coordinates (-10, -5).
Thus, the coordinates of A' and B' after the dilation are A' (5, 10) and B' (-10, -5).
The correct answer is option 4: A' (5, 10) and B' (-10, -5).