Question

The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is

Options

• −2 : 3

•  −3 : 2

•  3 : 2

• 2 : 3

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 + n y_1)/(m + n ))`

Here it is said that the point (4, 5) divides the points A(2,3) and B(7,8). Substituting these values in the above formula we have,

`(4,5) = ((m(7)+n(2))/(m+n) , (m(8)+n(3))/(m+n))`

Equating the individual components we have,

           `4 = ((m (7) + n(2) )/(m+n)) `

`4m + 4n = 7m + 2 n`

         `3m = 2n `

          `m/n = 2/3`