Question

dis Find the wordinates of the point which divides to
joining (-1; 2) & (4, -3) in the ratio 2.3.​

Answer 1

Solution :-

We need to find :-

The coordinates of the point which divides the line joining (-1 , 2) and (4 , -3) in the ratio 2 : 3.

We can find the coordinates of the point using section formula.

According to the section formula :-

$\bullet \bf \ x \ coordinate = \dfrac{mx_2+nx_1}{m+n} \\\\\bullet \ y \ coordinate = \dfrac{my_2+ny_1}{m+n}$

Here :-

$\bullet \sf \ x_1 = -1 \\\\\bullet \ y_1 = 2 \\\\\bullet \ x_2 = 4 \\\\\bullet \ y_2 = -3 \\\\\bullet \ m = 2 \\\\\bullet \ n = 3$

x coordinate :-

$\longrightarrow \sf \dfrac{(2 \times 4) +( 3 \times-1 ) }{2+3} \\\\\longrightarrow \dfrac{8-3}{5}\\\\\longrightarrow \dfrac{5}{5} \\\\\longrightarrow \bf 1$

y coordinate :-

$\longrightarrow \sf \dfrac{( 2\times -3)+ ( 3 \times 2)}{2+3} \\\\\longrightarrow \dfrac{-6+6}{5}\\\\\longrightarrow \dfrac{0}{5} \\\\\longrightarrow \bf 0$

Coordinates of the point = ( 1 , 0 )