Question

Find the coordinates of a point which divides the time joining the points (-3-4)and(2,1)externally in the ratio of 3:2

Answer 1

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 $\sf (x_1 ,y_1)\:\:\&\:\:(x_2,y_2)$ externally in the ratio m : n are given by:

$\sf \: (x \: , \: y) = \bigg( \dfrac{mx _{2} - nx_1}{m - n} \: \:,\: \: \dfrac{my_2 - ny_1}{m - n} \bigg)$

Let,

• $\sf x_1$ = - 3

• $\sf x_2$ = 2

• $\sf y_1$ = - 4

• $\sf y_2$ = 1

• m = 3

• n = 2

Hence,

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

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