Question

find the co- ordinates of the point of trisection of line A B given A(3,3) and B(14,6)​

Answer 1

Here ,

Line segment AB is divided into three equal parts such that

AP = PQ = BQ

let ,

AP: PB = 1 : 2

AP: PB = m: n = 1 : 2

let ,P = ( x,y )

A= ( x1, y1) = (3,3)

B= (x2, y2) = ( 14 ,6)

x = mx2+nx1 / m+ n ; y = my2+ny1/ m+n

= 1*14+2*3/1+2. = 1*6+2*3/ 1+2

= 14+6/3. = 6+6/3

= 20/3. =12/3= 4

Thus , coordinate of point P is ( 20/3 ,4 ).