Question

Find the coordinates of the points which divides the line segment joining the points (4,-3) and (8,5) in ration 3:1 internally.​

Answer 1

SOLUTION :-

Let ( x , y ) be the coordinates of the point which divides the line segment joining the points ( 4 , -3 ) and ( 8 , 5 ) in the ratio 3 : 1 internally.

We can find the coordinates using section formula,

$\longrightarrow\bf (x ,y ) = \left( \dfrac{mx_2+nx_1}{m+n } ,\dfrac{my_2+ny_1}{m+n} \right)$

Here,

$\bullet\sf \ x_1=4\\\\\bullet \ x_2=8\\\\\bullet\ y_1=-3\\\\\bullet \ y_2= 5 \\\\\bullet \ m = 3\\\\\bullet \ n = 1$

$\longrightarrow \sf x= \dfrac{( 3\times 8)+(1 \times4)}{3+1}\\\\\longrightarrow x= \dfrac{24+4}{4} \\\\\longrightarrow x = \dfrac{28}{4} \\\\\longrightarrow \bf x = 7$

$\longrightarrow\sf y = \dfrac{(3\times 5)+(1\times -3)}{3+1} \\\\\longrightarrow y= \dfrac{15-3}{4} \\\\\longrightarrow y=\dfrac{12}{4} \\\\\longrightarrow \bf y = 3$

Coordinates of the point = ( 7 , 3 )