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Find the coordinates of the point which divides the join of \mathrm{A}(-1,7) and \mathrm{B}(4,-3). in the ratio 2: 3
CBSE | Class 10 | Coordinate Geometry | Exercise 16.2 | Maths | RS Aggarwal
Find the coordinates of the point which divides the join of \mathrm{A}(-1,7) and \mathrm{B}(4,-3). in the ratio 2: 3

The end points of \mathrm{AB} are \mathrm{A}(-1,7) and \mathrm{B}(4,-3).

=> \left(x_{1}=-1, y_{1}=7\right) and \left(x_{2}=4, y_{2}=-3\right)

m=2 and n=3

Let the required point be \mathrm{P}(\mathrm{x}, \mathrm{y}).

using section formula

\mathrm{x}=\frac{\left(\mathrm{mx}_{2}+\mathrm{n} \mathrm{x}_{1}\right)}{(\mathrm{m}+\mathrm{n})}, \mathrm{y}=\frac{\left(\mathrm{my}_{2}+\mathrm{ny}_{1}\right)}{(\mathrm{m}+\mathrm{n})}

\Rightarrow x=\frac{\{2 \times 4+3 \times(-1)\}}{2+3}, y=\frac{\{2 \times(-3)+3 \times 7\}}{2+3}

\Rightarrow x=\frac{8-3}{5}, y=\frac{-6+21}{5}

\Rightarrow \mathrm{x}=\frac{5}{5}, \mathrm{y}=\frac{15}{5}

=>  x=1 and y=3

Therefore, the coordinates of the required point are (1,3).

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