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The coordinates of a point (x,y) which divides the straight line joining two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ internally in the ratio $m_{1}$ and $m_{2}$ are

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x = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}, y = \frac{m_{1} y_{1} + m_{2} y_{2}}{m_{1} + m_{2}}

x = \frac{m_{1} x_{2} + m_{2} x_{1}}{m_{1} + m_{2}}, y = \frac{m_{1} y_{2} + m_{2} y_{1}}{m_{1} + m_{2}}

x = 0, y = 0

x = \frac{m_{1} x_{1} - m_{2} x_{2}}{m_{1} - m_{2}}, y = \frac{m_{1} y_{1} - m_{2} y_{2}}{m_{1} - m_{2}}

answer is B.

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Detailed Solution

It is given that the coordinates of a point (x,y) divides the straight line joining two points

(x_{1}, y_{1})

and

(x_{2}, y_{2})

internally in the ratio

m_{1}

and

m_{2}

.
This is the section formula, i.e. if a point divides the line segment

AB

joining given two points in given m:n ratio internally, then by section formula, the coordinates of a point are given as,

x = \frac{m x_{2} + n x_{1}}{m + n}

and

y = \frac{m y_{2} + n y_{1}}{m + n}

So the correct option is 2.

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