if the three consecutive vertices of parallelogram ABCD are A(1,-2) B(3,6) C(5,10) find the fourth vertex D?

Hello,

Join AC AND BD. LET THEM INTERSECT AT O (x,y) Let coordinates of D be (x1,y1)

In ||gm. ABCD, Diagonals bisect each other.

=> OA = OC AND OB = OD.

=> Coordinates of mid point of AC ie. O =  [ { (1+5) /2 } , {(-2 + 10) / 2} ] = (3, 4) ( BY mid point Formula,)

Coordinates of mid point of BD ie. O = { (3 + x1) / 2} , { (6 + y1) /2 } = (3, 4) (BY MID POINT FORMULA )

=> (3 + x1) / 2  = 3  and  (6+y1) / 2 = 4

=> x1 = 3  and  y1 = 2

Ans :- Coordinates of point D are (3,2)

Hope it helps !

Plz. thumbs up.

ANURAG.