Question

The x-axis divides the line segment joining the points (–4, –6) and (–1, 7) in the ratio ______.

Answer 1

The x-axis divides the line segment joining the points (–4, –6) and (–1, 7) in the ratio 6 : 7.

Explanation:

Let A = (–4, –6), B = (–1, 7) and let the x-axis meet AB at P, which divides AB in the ratio λ : 1 (AP : PB = λ : 1).

By the section formula the y-coordinate of P is `(7λ - 6)/(λ + 1)`.

Since P lies on the x-axis this y-coordinate = 0, so 7λ – 6 = 0 ⇒ λ = `6/7`.

Hence the ratio is 6 : 7 and the point of division is `(-34/13, 0)`