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.

Question

1. A′ (−8, 2) and B′ (−2, 6)
2. A′ (−5, −2) and B′ (−2, 6)
3. A′ (−8, 2) and B′ (2, −6)
4. A′ (8, −2) and B′ (2, −6)

Answer 1

To find the coordinates of points \( A' \) and \( B' \) after a dilation with a scale factor of 2 from the origin, we multiply each coordinate of points \( A \) and \( B \) by the scale factor.

1. For point \( A(-4, 1) \): \[ A' = (2 \times -4, 2 \times 1) = (-8, 2) \]

2. For point \( B(-1, 3) \): \[ B' = (2 \times -1, 2 \times 3) = (-2, 6) \]

Thus, the coordinates after dilation are: \[ A'(-8, 2) \quad \text{and} \quad B'(-2, 6) \]

This corresponds to option 1:

1. \( A' (-8, 2) \) and \( B' (-2, 6) \)