Line AB contains point A(−4, 1) and point B (−1, 3) . Find the coordinates of A′ and B′ after a dilation with a scale factor of 2 with a center point of dilation at the origin.
1.A′ (−5, −2) and B′ (−2, 6)
2.A′ (−8, 2) and B′ (2, −6)
3.A′ (8, −2) and B′ (2, −6)
4.A′ (−8, 2) and B′ (−2, 6)
To find the coordinates of A' and B' after a dilation with a scale factor of 2 and a center point of dilation at the origin, we can multiply the x and y coordinates of A and B by 2.
Coordinates of A' = (2 * x-coordinate of A, 2 * y-coordinate of A)
Coordinates of B' = (2 * x-coordinate of B, 2 * y-coordinate of B)
Using this formula, we can calculate the coordinates of A' and B':
Coordinates of A' = (2 * -4, 2 * 1) = (-8, 2)
Coordinates of B' = (2 * -1, 2 * 3) = (-2, 6)
Therefore, the correct answer is option 4: A' (-8, 2) and B' (-2, 6).