Question

Find the equations of the straight lines which pass through the origin and trisect the portion of the straight line 2x + 3y = 6 which is intercepted between the axes.

Answer 1

To find:

Equations of the straight lines which pass through the origin and trisect the portion of the line which is intercepted between the axes. 

Assuming:

The line 2x + 3y = 6 intercept the x-axis and the y-axis at A and B, respectively. 

Explanation: 

At x = 0 we have,

3y + 0 = 6 

⇒ 3y = 6 

⇒ y = 2 

At y = 0 we have, 2x + 0 = 6 

⇒x = 3 

A = (3, 0) and B = (0, 2) 

Let y = m₁x and y = m₂x pass through origin trisecting the line 2x + 3y = 6 at P and Q. 

AP = PQ = QB 

Let us find the coordinates of P and Q using the section formula

Hence, the equation of line is x – 3y = 0 and 4x – 3y = 0