Question

Show that the line segment joining the points (-3, 10) and (6, -5) is trisected by the coordinates axis.

Answer 1

Let the coordinates of two points x-axis and y-axis be P (x, O) and G (0, y) respectively.

Let P divides AB in the ratio k : 1.

Coordinates of P are 

P (x , 0) = P `((6"k" - 3)/("k" + 1) , (- 5 "k" + 10)/("k" + 1))`

⇒ 0 = `(- 5 "k" + 10)/("k" + 1)`

⇒ 5 k = 10

⇒ k = 2

Hence P divides AB in the ratio 2: 1. 

Let Q divides AB in the ratio k₁ : 1. 

Coordinates of Q are, 

Q (0 , y) = Q `((6"k"_1 - 3)/("k" + 1) , (-5"k" + 10)/("k" + 1))`

`=> 0 = (6"k"_1 - 3)/("k" + 1)`

⇒ 6k₁ = 3

⇒ `"k"_1 = 1/2`

Hence Q divides AB in the ratio 1: 2

Hence proved, P and Q are the points of trisection.