Question

Find the ratio in which the points P (3/4, 5/12) divides the line segments joining the points A(1/2 , 3/2) and B(2, -5).

Answer 1

The ratio is 1:5

Let the required ratio be m:n.

First point is A (3/4, 5/12) , second point is B (2,-5)

According to the section formula,

(x,y) = ([mx₂+nx₁]/[m+n],[my₂+ny₁]/[m+n])

where  (x,y)  is the coordinate of the point which divides the two points.

(x₁,y₁) is the coordinate of A and (x₂,y₂) is the coordinate of B.

Putting the respective values, we equate the x-coordinate as

3/4 = (2m+n/2)/(m+n)

⇒ (4m+n)/[2(m+n)] = 3/4

⇒ 6m + 6n = 16m +4n

⇒ 10m = 2n

⇒ m/n = 2/10 = 1/5

So, the ratio is 1:5