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Question
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
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Solution
Let P( x , y) be the point which divide the line segment joining A (2, 3) and B (3, 4) in the ratio 1: 5.
Now according to the section formula if point a point P divides a line segment joining` A( x_1 , y_ 1) ` and `B ( x_ 2 , y_ 2 )` in the ratio m: n internally than,`
`P ( x , y ) = ( ( nx_ 1 + mx _ 2 ) /( m + n ) , ( ny_1 + my _ 2 ) /( m+ n ) )`
Now we will use section formula as,
`P ( x , y ) = ((5(2) + 3) /( 5 + 1) , ( 5 ( 3 ) + 4) /(4+1))`
` = (13/6 , 19/6)`
So co-ordinate of P is ` = (13/6 , 19/6)`
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