Question

Find the coordinates of point P, if P divides the line segment joining the points A(-2, -5), B(4, 3) in the ratio 3:4​

Answer 1

$\maltese\LARGE\textsf{\underline{ SoLuTioN :-}}$

$\large\textsf{ }$

$\sf\longrightarrow{ \: Here \: \: \: we \: \: \: have \: \: \: to \: \: \: use \: \: \: the \: \: \: section \: \: \: formula \: : - }$

$\large\textsf{ }$

$\boxed{\begin{array}{c}\sf\color{purple} \: x \: = \: \cfrac{m x_{2} \: + \: n x_{1} }{m \: + \: n \: } \\ \\ \\ \sf \color{purple} \: y \: = \: \cfrac{m y_{2} \: + \: n y_{1} }{m \: + \: n \: } \end{array}}\small\textsf{ ------( Section \; \; Formula )}$

$\large\textsf{ }$

Let ,

A ( - 2 , - 5 ) = x₁ , y₁

B ( 4 , 3 ) = x₂ , y₂

P = ( x , y )

$\large\textsf{ }$

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$\sf \: \therefore \: x \: = \: \cfrac{3 \times 4 \: + \: 4 \times ( - 2)}{3 + 4} \\ \\ \\ \sf = \: \frac{12 \: + \: ( - 8)}{7} \\ \\ \\ \sf= \: \frac{12 \: - \: 8}{7} \\ \\ \\ \: \therefore \color{red}\boxed { \sf\: x \: = \: \frac{4}{7} }$

$\large\textsf{ }$

$\sf \: \therefore \: y \: = \: \cfrac{3 \times 3 \: + \: 4 \times ( - 5)}{3 + 4} \\ \\ \\ = \sf \: \frac{9 \: + \: (- 12)}{7} \\ \\ \\ = \: \sf \frac{9 \: - 12}{7} \\ \\ \\ \: \therefore \color{red} { \boxed { \sf\: y \: = \: \frac{ - 3}{7} }}$

$\large\textsf{ }$

${\therefore { \: \: \sf{\: \: the \: \: \: co - ordinates \: \: \: of \: \: \: point \: \: \: P \: \: \: are \: }}}$

$\qquad\tt{:}\longrightarrow\; \; \; \boxed{{\large\textsf\color{green}{P = \left(\cfrac{\large\textsf{4}}{\large\textsf{7}} \; \; ,\; \; \cfrac{\large\textsf{- 3}}{\large\textsf{7}} \right) }}}$

Answer 2

Explanation:

Given:

ABAP=73

⇒AP=73AB

⇒AP=73(AP+PB)

⇒7AP=3AP+3PB

⇒7AP−3AP=3PB

⇒4AP=3PB

⇒PBAP=43

Hence, the point P divides AB in the ratio 3:4

(x,y)=(m1+m2m1x2+m2x1,m1+m2m1y2+m2y1)...(i)

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