Question

Find the coordinates of the point which divides the join of A(-1, 7) and B(4, -3) in the ratio 2 : 3.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Coordinate\:of\:p=(1,3)}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given: }} \\ \tt: \implies Coordinate \: of \: a = ( - 1,7) \\ \\ \tt: \implies Coordinate \: of \: b= (4, - 3) \\ \\ \tt: \implies Ratio\:(m :n) = 2 : 3 \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies Coordinate \: of \: p = (x,y)$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies x = \frac{m x_{2} + n x_{1}}{m + n} \\ \\ \tt: \implies x = \frac{2 \times4 + 3 \times - 1 }{2 + 3} \\ \\ \tt: \implies x = \frac{8 - 3}{5} \\ \\ \tt: \implies x = \frac{5}{5} \\ \\ \green{\tt: \implies x = 1} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies y = \frac{m y_{2} + n y_{1}}{m + n} \\ \\ \tt: \implies y = \frac{2 \times - 3+ 3 \times 7 }{ 2 + 3} \\ \\ \tt: \implies y= \frac{ - 6 + 21}{5} \\ \\ \tt: \implies y = \frac{15}{5} \\ \\ \green{\tt: \implies y = 3} \\ \\ \green{\tt \therefore Coordinate \: of \: p = (1,3)}$

Answer 2

$\huge\bold\green{Question}$

Find the coordinates of the point which divides the join of A(-1, 7) and B(4, -3) in the ratio 2 : 3.

$\huge\bold\green{Answer}$

Acc. to the question we have given :-

°•° Given Coordinateof a = (−1,7)

°•° Given Coordinate of b = (4,−3)

°•° Given Ratio (m:n) = 2:3

So , according to the question we have to find out the

Coordinate of “ p ”

let the Coordinate of “ p ” will he ( x , y )

So , as said in question let's find out the points

$\begin{lgathered}\bold{So \: we \: know \: that\: the : section\: formula\:is} \\ \sf x = \frac{m x_{2} + n x_{1}}{m + n} \\ \\ \sf x = \frac{2 \times4 + 3 \times - 1 }{2 + 3} \\ \\ \sf x = \frac{8 - 3}{5} \\ \\ \sf x = \cancel\frac{5}{5} \\ \\ \sf x = 1 \\ \\ \sf y = \frac{m y_{2} + n y_{1}}{m + n} \\ \\ \sf y = \frac{2 \times - 3+ 3 \times 7 }{ 2 + 3} \\ \\ \sf y= \frac{ - 6 + 21}{5} \\ \\ \sf y = \frac{15}{5} \\ \\ \sf y = 3 \\ \\ \implies\sf {Hence Coordinate \: of \: p = (1,3)}\end{lgathered}$

So, the required coordinate of p is ( 1 ,3 )