C(3,0) and D(3,1) are the points of trisection of a line segment AB . Find the respective coordinates of A and B .
(a) (3,2) , (3,0) `" "` (b) (3,-1) , (3,2) `" "` (c) (-3,1) , (3,2) `" "` (d) None of these

Explanation

Let A and B be `(a_(1) , b_(1))` and `(a_(2) , b_(2))` . Given , C(3,0) and D( 3, 1) are the points of trisection of AB.

`implies C` is the mid-points of AD and D is the mid-points of CB.
`implies (3,0) = ((a_(1) +3)/(2) , (b_(1) + 1)/(2))`
`implies a_(1) = 3` and `b_(1) = -1`
Also , `(3,1) = ((3+ a_(2))/(2) , (0+b_(2))/(2))`
`implies a_(2) = 3 ` and `b_(2) = 2`.
`therefore` The coordinates of A and B are (3, -1) and (3,2) .