Question

Find the coordinates of a point P on the line segment joining A(1, 2) and B(6, 7) in such a way that AP = `2/5` AB

Answer 1

Let the point A(1, 2) and B(6, 7)

AP = `2/5` AB

`"AP"/"PB" = 2/5`

∴ AP = 2, PB = 5 – 2 = 3

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 = 2, n = 3, x₁ = 1, x₂ = 6, y₁ = 2, y₂ = 7

The point P is (3, 4)

= `((2 xx 6 + 3 xx 1)/(2 + 3), (2 xx 7 + 3 xx 2)/(2 + 3))`

= `((12 + 3)/5, (14 + 6)/5)`

= `(15/5, 20/5)`

= (3, 4)