Question

find the coordinate of the point which divides the line segment joining the point (3, -3) and 8,4 in the ratio 2:1​

Answer 1

Given :

Coordinates of the line segment = ( 3 , -3 ) and ( 8 , 4 )

Ratio = 2 : 1

To find :

The coordinates of point that divides the given segment in the given ratio .

Solution :

If coordinates of line segment is ( x$_1$ , y$_1$ ) and ( x$_2$ , y$_2$ ) and the ratio in which it is divided by a point ( x , y ) is m$_1$ : m$_2$ ,

then ,

( x , y ) = [ (m$_1$x$_2$ + m$_2$x$_1$) / (m$_1$ + m$_2$) , (m$_1$y$_2$ + m$_2$y$_1$) / (m$_1$ + m$_2$) ]

now ,

( x , y ) = [ ( 2*8 + 1*3 ) / ( 2 + 1 ) , ( 2*4 - 1*3 ) / ( 2 + 1 ) ]

=> ( x , y ) = ( 19 / 3 , 5 / 3 )

The point ( 19/3 , 5/3 ) divides the line segment joining the point ( 3 , -3 ) and ( 8 , 4 ) in the ratio 2:1​ .

Answer 2

the coordinate of the point which divides line segment joining the point (-3, 3) and (3, -3) in the ratio 2:1