Question

Point A is at –4 and point B is at 6. Which describes one way to find the point that divides AB into a 3:2 ratio?



For a ratio of 3:2, divide AB into 3 equal parts. Each equal part is 3 units, so the point that divides AB into a 3:2 ratio is 0.
For a ratio of 3:2, divide AB into 3 equal parts. Each equal part is 3 units, so the point that divides AB into a 3:2 ratio is 3.
For a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 1.
For a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 2.

Answer 1

The correct choice is the fourth.

Explanation: AB = 6 - (−4) = 10. Divide into 5 equal parts (3:2 → 3+2 =5), each part = 10/5 = 2. AP = 3 parts = 3·2 = 6, so P = −4 + 6 = 2.

(Or use the section formula: P = (2·(−4) + 3·6)/5 = (−8+18)/5 = 2.)