Question

In what radio does the point ( -4 , 6 ) divide the line segment joining the points A (-6,10) and B (3,-8)

Answer 1

Let P(-4,6) divided AB in the ratio k : 1.

Here, (x₁,y₁) = (-6,10), (x₂,y₂) = (3,8), m = k, n = 1.

Section formula:

Coordinates of P = (3k - 6/k + 1, -8k + 4/k + 1)

⇒ (-4,6) = (3k - 6/k + 1, -8k + 4/k + 1).

So,

⇒ -4 = (3k - 6)/(k + 1)

⇒ -4(k + 1) = 3k - 6

⇒ -4k - 4 = 3k - 6

⇒ -4k - 3k = -6 + 4

⇒ -7k = -2

⇒ k = 2/7.

Hope this helps!