Question

Find the coordinates of the points which divide PQ in the ratio of 2:3 internally and externally. The coordinates of P and Q are (2,-1) and (-3,4).


please,Answer and explain it properly

Answer 1

The coordinates of point when $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are divided in $A:B$

• $Internally:\,\,\,[(\frac{Ax_{2}+Bx_{1}}{A+B}), (\frac{Ay_{2}+By_{1}}{A+B})]$
• $Externally:\,\,\,[(\frac{Ax_{2}-Bx_{1}}{A-B}), (\frac{Ay_{2}-By_{1}}{A-B})]$

Let the coordinates of the required point be $P(m, n)$,

• For the internal Division,

$m =(\frac{2(-3)+3(-1)}{2+3})= \frac{-9}{5}\\n = (\frac{2(-5)+3(2)}{2+3})= \frac{-4}{5}\\\\\implies \boxed{\bf P(\frac{-9}{5}, \frac{-4}{5})}$

• For the external Division,

$m =(\frac{2(-3)-3(-1)}{2-3})= \frac{-3}{-1}=3\\n = (\frac{2(-5)-3(2)}{2-3})= \frac{-16}{-1}= 16\\\\\implies \boxed{\bf P(3, 16)}$

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