Question

find the coordinates of the point q which divides externally the join of a(3,4) and b(-6,2) in ratio 3:2​

Answer 1

Answer:

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Answer 2

Answer:

Answer:

Given:

A point divides the line segment joining the points ( - 3 , - 4) and (2 , 1) externally in the ratio 3 : 2.

Using section formula;

That is, the co - ordinates of a point which divides the line segment joining the points \sf (x_1 ,y_1)\:\:\&\:\:(x_2,y_2)(x 1 ,y 1 )&(x2 ,y 2 ) externally in the ratio m : n are given by:

$\sf \: (x \: , \: y) = \bigg( \dfrac{mx _{2} - nx_1}{m - n} \: \:,\: \: \dfrac{my_2 - ny_1}{m - n} \bigg)(x,y)=( m−nmx 2 −nx 1 , m−nmy 2−ny1 )$

Let,

\sf x_1x 1 = - 3\sf x_2x 2 = 2\sf y_1y 1 = - 4\sf y_2y2 = 1

m = 3

n = 2

Hence,

$\begin{gathered}\sf \implies \: (x \: , \: y) = \bigg( \dfrac{(3)(2) - (2)( - 3)}{3 - 2} \: \:, \: \: \dfrac{(3)(1) - (2)( - 4)}{3 - 2} \bigg) \\ \\ \sf \implies \: (x \:, \: y) = \bigg( \dfrac{6 + 6}{1} \: \:, \: \: \dfrac{3 + 8}{1} \bigg) \\ \\ \sf \implies \large{ \red{ (x \: , \: y) = (12 \: , \: 11)}}\end{gathered}$

⟹(x,y)=( 3−2(3)(2)−(2)(−3) , 3−2(3)(1)−(2)(−4) )

⟹(x,y)=( 16+6 , 13+8 )⟹(x,y)=(12,11)

Therefore, the co - ordinates of the point are (12 , 11).