Question

Find the coordinates of the point which divides the line segment joining the points A(4, −3) and B(9, 7) in the ratio 3 : 2

Answer 1

A line divides internally in the ratio m : n

The point P = `(("m"x_2 + "n"x_1)/("m" + "n"), ("m"y_2 + "n"y_1)/("m" + "n"))`

m = 3, n = 2, x₁ = 4, x₂ = 9, y₁ = −3, y₂ = 7

= `((3 xx 9 + 2 xx 4)/(3 + 2), (3 xx 7 + 2(-3))/(3 + 2))`

= `((27 + 8)/5, (21 - 6)/5)`

= `(35/5, 15/5)`

= (7, 3)