Find the ratio in which the point P(x, 2) divides the join of A(12, 5) and B(4, -3).

Question

Philoid · Accepted Answer

Let the point P(x, 2) divides the join of A(12, 5) and B(4, -3) in the ratio of m:n.

fig.2

Recall that if (x,y) ≡ (a,b) then x = a and y = b

∴ assume that

(x,y) ≡ (x,2)

(x₁,y₁) ≡ (12,5)

and, (x₂,y₂) ≡ (4,-3)

Now, Using Section Formula-

⇒ 2m + 2n = -3m + 5n

⇒ 5m = 3n

∴ m:n = 3:5

Thus, the required ratio is 3:5.