Question

Point C divides the line segment whose points are A(4, –6) and B(5, 9) in the ratio 2:1. Find the coordinates of C.

Answer 1

Given points are A(4, –6) and B(5, 9) and the ratio is 2:1.

Let the coordinates of C be (x, y).

Then, by the section formula,

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

= `(2 xx 5 + 1 xx 4)/(2 + 1)`

= `(10 + 4)/3`

= `14/3`

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

= `(2 xx 9 + 1 xx (-6))/(2 + 1)`

= `(18 - 6)/3`

= `12/3`

= 4

As a result, the coordinates of point C are `(14/3, 4)`.