Question

The point Q divides segment joining A(3, 5) and B(7, 9) in the ratio 2 : 3. Find the X-coordinate of Q

Answer 1

Let the co-ordinates of point Q be (x, y) and A (x₁, y₁), B (x₂, y₂) be the given points.

Here, x₁ = 3, y₁ = 5, x₂ = 7, y₂ = 9, m = 2, n = 3

∴ By section formula,

x = `("m"x_2 + "n"x_1)/("m" + "n")`

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

= `(14 + 9)/5`

= `23/5`

y = `("m"y_2 + "n"y_1)/("m" + "n")`

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

= `(18 + 15)/5`

= `33/5`

∴ The co-ordinates of point Q are `(23/5, 33/5)`.