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Distance between Two Points on the Same Coordinate Axes

If a point Px...

Question

If a point P(x, y) divides the line segment joining , A $(x_{1}, y_{1})$ and B $(x_{2}, y_{2})$ in the ratio $m_{1}$ and $m_{2}$ then the coordinates of P are $(p \frac{m_{1} x_{2} + m_{2} x_{1}}{m_{1} + m_{2}}, q \frac{m_{1} y_{2} + m_{2} y_{1}}{m_{1} + m_{2}})$ then p+q =

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Solution

Given that point $P (x, y)$ divides the line segment joining $A (x_{1} y_{1})$ $B (x_{2} y_{2})$ in the ratio $m_{1} : m_{2}$ then the coordinates of P can be obtained using the section formula.
( Diagram )
Using section formula we can write :
$\Rightarrow (x, y) \equiv (\frac{m_{1} x_{2} + m_{2} x_{1}}{m_{2} m_{2}}, \frac{m_{1} y_{2} + m_{2} y_{2}}{m_{1} + m_{2}})$
Hence, the answer is $(\frac{m_{1} x_{2} + m_{2} x_{1}}{m_{2} m_{2}}, \frac{m_{1} y_{2} + m_{2} y_{2}}{m_{1} + m_{2}}) .$

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Distance between Two Points on the Same Coordinate Axes

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