Question

If point P (- 4,6) divide the line segment AB with A(- 6 ,10) in the ratio 2 : 1 then coordinates of point B =? *

Answer 1

SOLUTION :-

Given that,

The point P ( -4 , 6 ) divide the line segment AB with A ( -6 , 10 ) in the ratio 2 : 1 .

Let,

Coordinates of B = ( a , b )

We can use section formula to find the coordinates of B .

According to section formula,

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

Here,

$\bullet\sf \ x= -4 \\\\\bullet \ y = 6 \\\\\bullet \ x_1=-6\\\\\bullet \ x_2= a \\\\\bullet \ y_1=10 \\\\\bullet \ y_2= b$

$\bullet\sf \ m = 2\\\\\bullet \ n = 1$

$\longrightarrow\sf x= \dfrac{mx_2+nx_1}{m+n} \\\\\longrightarrow -4 = \dfrac{(2\times a) + (1 \times -6 )}{2+1}\\\\\longrightarrow -4 = \dfrac{2a-6}{3} \\\\\longrightarrow 2a-6 = -12 \\\\\longrightarrow 2a= - 6 \\\\\longrightarrow \bf a = -3$

$\longrightarrow\sf y=\dfrac{my_2-ny_1}{m+n} \\\\\longrightarrow 6= \dfrac{(2\times b )+(1 \times 10)}{2+1} \\\\\longrightarrow 6=\dfrac{2b+10}{3} \\\\\longrightarrow 2b+10 = 18 \\\\\longrightarrow 2b = 8 \\\\\longrightarrow\bf b = 4$

Coordinates of the point B = ( -3 , 4 )