Question

if pointp (2,3)divides the line joining the points (5,6)and(8,9),then the ratio is.

Answer 1

The ratio in which P(2, 3) divides (5, 6) and (8, 9) is -1:2.

• Let the ratio be m:1
• Given

               P(2, 3) A(5, 6) B(8, 9)

• Using section formula, we get

              $(2,3)=(\frac{mx_{2}+x_{1}}{m+1},(\frac{my_{2}+y_{1}}{m+1})$

              $(2,3)=(\frac{m(8)+5}{m+1},\frac{m(9)+6}{m+1})$

• Comparing coordinates, we get

              $\frac{8m+5}{m+1}=2$

               8m + 5 = 2(m + 1)

               8m + 5 = 2m + 2

               8m - 2m = 2 - 5

               6m = - 3

               2m = -1

                m = -1/2

         ∴ P divides AB in the ratio -1:2