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Section Formula

The co-ordina...

Question

The co-ordinates 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

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}}

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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}}

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x=0,y=0

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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}}

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Solution

The correct option is A $x = \frac{m_{1} x_{2} + m_{2} x_{1}}{m_{1} + m_{2}}, y = \frac{m_{1} y_{2} + m_{2} y_{1}}{m_{1} + m_{2}}$
This is the Section formula, i.e. If a point divides the line segment $A B$ joining given two points in given m:n ratio internally, then by section formula, the co-ordinates of a point are given as

$= (\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})$

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Similar questions

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B (x_{2}, y_{2})

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m_{1}

m_{2}

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1_{2} x + m_{2} y + n_{2} = 0

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l_{1} l_{2} + m_{1} m_{2} =

m₁ and m₂ are the slope of two perpendicular lines, if

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