Question

Find the coordinates of point which divides the join of (-1,7) and (4,-3) in

the ratio 2:3​

Answer 1

$\bf \purple{Given}\begin{cases}&\sf{Coordinates\:of\:P=\bf{(-1,7)}} \\ \\ &\sf{Coordinates\:of\:Q=\bf{(4,-3)}} \\ \\ &\sf{Ratio=\bf{2:3}}\end{cases}$

To FinD:-

Coordinate of point PQ.

SolutioN:-

Here we have to use section formula.

We know that,

$\\ \normalsize{\pink{\underline{\boxed{\sf{(x,y)=\Bigg\lgroup\dfrac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\dfrac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}}\Bigg\rgroup}}}}}$

$\sf {Here}\begin{cases}&\sf{(x,y)=\bf{(PQ)}} \\ &\sf{m_{1}=\bf{2}} \\ &\sf{m_{2}=\bf{3}} \\ &\sf{x_{1}=\bf{-1}} \\ &\sf{x_{2}=\bf{4}} \\ &\sf{y_{1}=\bf{7}} \\ &\sf{y_{2}=\bf{-3}}\end{cases}$

• Putting the values,

$\\ :\normalsize\implies{\sf{(x,y)=\Bigg\lgroup\dfrac{2\times4+3\times(-1)}{2+3},\dfrac{2\times(-3)+3\times7}{2+3}\Bigg\rgroup}}$

$\\ :\normalsize\implies{\sf{(x,y)=\Bigg\lgroup\dfrac{8+(-3)}{5},\dfrac{(-6)+21}{5}\Bigg\rgroup}}$

$\\ :\normalsize\implies{\sf{(x,y)=\Bigg\lgroup\dfrac{8-3}{5},\dfrac{-6+21}{5}\Bigg\rgroup}}$

$\\ \quad:\normalsize\implies{\sf{(x,y)=\Bigg\lgroup\dfrac{5}{5},\dfrac{15}{5}\Bigg\rgroup}}$

$\\ \quad\;\;\;:\normalsize\implies{\sf{(x,y)=\Bigg\lgroup\dfrac{\cancel{5}}{\cancel{5}},\dfrac{\cancel{15}}{\cancel{5}}\Bigg\rgroup}}$

$\\ \quad\quad\:\::\normalsize\implies{\sf{(x,y)=\lgroup1,3\rgroup}}$

$\\ \quad\quad\quad\quad\normalsize\therefore\boxed{\mathfrak{\purple{PQ=\lgroup1,3\rgroup}}}$

The coordinates of point PQ is (1,3) .