Question

If A(3, 5) and B(7, 9), point Q divides seg AB in the ratio 2 : 3, find the coordinates of point Q.

Answer 1

Let A(3, 5) ≡ (x₁, y₁), (7, 9) ≡ (x₂, y₂)

By section formula,

x co-ordinate of point Q = `(mx_2 + nx_1)/(m + n)`

= `(2 xx 7 + 3 xx 3)/(2 + 3)`

= `(14 + 9)/5`

= `23/5`

y co-ordinate of point Q = `(my_2 + ny_1)/(m + n)`

= `(2 xx 9 + 3 xx 5)/(2 + 3)`

= `(18 + 15)/5`

= `33/5`

∴ The coordinates of point Q are `(23/5, 33/5)`.