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.

Question

1. A′ (5, 10) and B′ (−10, −5)
2. A′ (1, 2) and B′ (−10, −5)
3. A′ (5, 10) and B′ (10, 5)
4. A′ (5, 10) and B′ (−2, −1)

Answer 1

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 formula for dilation:

\[ (x', y') = (k \cdot x, k \cdot y) \]

where \(k\) is the scale factor.

Given:

• Point A(1, 2)
• Point B(−2, −1)
• Scale factor \(k = 5\)

Let's calculate the coordinates of A' and B':

1. For point A(1, 2): \[ A' = (5 \cdot 1, 5 \cdot 2) = (5, 10) \]

2. For point B(−2, −1): \[ B' = (5 \cdot (-2), 5 \cdot (-1)) = (-10, -5) \]

Thus, after dilation, the coordinates are:

• A' = (5, 10)
• B' = (−10, −5)

The correct answer is: 1. A′ (5, 10) and B′ (−10, −5).