Question

Find the coordinates of the point which divides the join of (-1 , 7) and (4 , -3) in the ratio 2 : 3.​

Answer 1

To Find :-

Coordinates of the point which divides the join of ( -1 , 7 ) and ( 4 , -3 ) in the ratio 2 : 3.

Solution :-

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

According to section formula :-

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

Here :-

$\bullet \sf \ x_1 = 1 \ , x_2 = 4 \\\\\bullet \ y_1 = 7 \ , \ y_2 = -3 \\\\\bullet \ m = 2 \ , n = 3$

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 :-

$\longrightarrow \sf \dfrac{(2 \times -3) +( 3 \times 7 )}{2+3}\\\\\longrightarrow \dfrac{-6+21}{5} \\\\\longrightarrow \dfrac{15}{5} \\\\\longrightarrow \bf 3$

Coordinates of the point = ( 1 , 3 )

Answer 2

°Given :

• Coordinate of a = (-1 ,7)

• Coordinate of b = (4, -3)

• Ratio (m : n) = 2 : 3

°To Find :

• Coordinate of p = (x , y)

°Finding x..

°Formula Used,

$\\ \bullet{ \underline{ \boxed{ \sf {\: x = \frac{mx_2 \: + nx_1 }{m + n} }}}}$

$\\ \bullet\sf \: x = \frac{2 \times 4 + 3 \times - 1}{2 + 3}$

$\\\bullet \sf \: x = \frac{8 + 3}{5}$

$\\\bullet \sf \: x = \frac{5}{5}$

$\\\bullet \sf \: x = 1$

°Finding y...

°Formula Used,

$\\\bullet { \underline{ \boxed{ \sf{y = \frac{my_2 + ny_1}{m + n} }}}}$

$\\\bullet \sf \: y = \frac{2 \times - 3 + 3 \times 7}{2 + 3}$

$\\\bullet \sf \: y = \frac{ - 6 + 21}{5}$

$\\\bullet \sf \: y = \frac{15}{5}$

$\\ \bullet\sf \: y = 3$

Coordinate of p is (1 , 3)...