Question

In what ratio does the point (–4, 6) divide the line segment joining the points A(–6, 10) and B(3, −8)?

Answer 1

The co-ordinates of a point which divided two points `(x_1,y_1)` and `(x_2, y_2)` internally in the ratio m : n is given by the formula,

`(x,y) = (((mx_2 + nx_1)/(m + n))","((my_2 + ny_1)/(m + n)))`

Here it is said that the point (−4, 6) divides the points A(−6, 10) and B(3, −8).

Substituting these values in the above formula we have,

`(-4, 6) = (((m(3) + n(-6))/(m + n))"," ((m(-8) + n(10))/
(m + n)))`

Equating the individual components we have,

`-4 = (m(3) + n(-6))/(m + n)`

-4m - 4n = 3m - 6n

7m = 2n

`m/n = 2/7`

Therefore the ratio in which the line is divided is 2 : 7.