Question

Find the coordinates of the points which divide the line joining (1, 6) and (5, 2) into three equal parts.

Answer 1

Let P, Q be two points on the line AB.

Then AP : PB = 1 : 2 and AQ : QB = 2 : 1

AP : PB = 1 : 2 , so coordinate of P is

Coordinate of x = \(1+\frac{1}{3}(5-1)=1+\frac{1}{3}\times4=\frac{7}{3}\)

Coordinate of y = \(6+\frac{1}{3}(2-6)=6-\frac{1}{3}\times4=\frac{14}{3}\)

Coordinate of P is \((\frac{7}{3},\frac{14}{3})\)

AQ : QB = 2 : 1 , so coordinate of Q is

Coordinate of x = \(1+\frac{2}{3}(5-1)=1+\frac{2}{3}\times4=\frac{11}{3}\)

Coordinate of y = \(6+\frac{2}{3}(2-6)=6-\frac{2}{3}\times4=\frac{10}{3}\)

Coordinate of Q is \((\frac{11}{3},\frac{10}{3})\)