Question

Given points (0, 0) and (3, 6), find the point which partitions the segment into 3:2

Please explain?

Answer 1

Point P partitions segment AB in a m:n ratio.

Use Section rormula.

If point P partitions AB in a m:n ratio, then the coordinates of point P are:

x coordinate = ( m ∙ x2 + n ∙ x1 ) / ( m + n )

y coordinate = ( m ∙ y2 + n ∙ y1 ) / ( m + n )


In this case:

x1 = 0 , x2 = 3 , y1 = 0 , y2 = 6 , m = 3 , n = 2

So:

x = ( m ∙ x2 + n ∙ x1 ) / ( m + n )

x = ( 3 ∙ 3 + 2 ∙ 0 ) / ( 3 + 2 )

x = 9 / 5


y = ( m ∙ y2 + n ∙ y1 ) / ( m + n )

y = ( 3 ∙ 6 + 2 ∙ 0 ) / ( 3 + 2 )

y = 18 / 5


P ( 9 / 5 , 18 / 5 )