In what ratio does the point C(4, 5) divide the join of A(2, 3) and B(7, 8)?

Question

Philoid · Accepted Answer

Let the ratio in which the point C(4, 5) divide the join of A(2, 3) and B(7, 8) be m:n.

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

Let (x,y) ≡ (4,5)

(x₁,y₁) ≡ (2,3)

and, (x₂,y₂) ≡ (7,8)

Now, Using Section Formula-

⇒ 4m + 4n = 7m + 2n

⇒ 3m = 2n

∴ m:n = 2:3

Thus, the required ratio is 2:3.