Question

In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)?

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 + 2))","((my_2 + ny_1)/(m + n)))`

Here it is said that the point `(-5, -21/5)` divides the points (-3,-1) and (-8,-9). 

Substituting these values in the above formula we have,

`(-5, -21/5) = (((m(-8) + n(-3))/(m + n))","((m(-9) + n(-1))/(m+ n)))`

Equating the individual components we have,

`-5 = (m(-8) + n(-3))/(m + n)`

-5m - 5n = -8m - 3n

3m = 2n

`m/n = 2/3`

Therefore the ratio in which the line is divided is 2:3