Question

Find the coordinates of point P if P divides the line segment joining the points A(–1, 7) and B(4, –3) in the ratio 2 : 3.

Answer 1

Let (x₁, y₁) = (–1, 7) and (x₂, y₂) = (4, –3), m : n = 2 : 3.

According to the section formula,

`x = (mx_2 + nx_1)/(m + n)`

`x = (2 xx 4 + 3 xx (-1))/(2 + 3)`

`x = (8 - 3)/5`

`x = 5/5`

∴ x = 1

`y = (my_2 + ny_1)/(m + n)`

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

`y = (-6 + 21)/(5)`

`y = (15)/(5)`

∴ y = 3

∴ The coordinate of points p is (1, 3).