Question

Given a line segment AB joining the points A (-4, 6) and B (8, -3). Find:

(i) the ratio in which AB is divided by the y-axis

(ii) find the coordinates of the point of intersection

(iii) the length of AB.

Answer 1

(i) Let the required ratio be m1 : m2

Consider A(-4, 6) = (x₁, y₁); B(8, −3) = (x₂ , y₂) and let

P(x, y) be the point of intersection of the line segment and the y-axis

By section formula, we have,

(iii) The length of AB = distance between two points A and B.

The distance between two given points

A(x₁ , y₁) and B (x₂ , y₂) is given by,