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

## CERTIFIED ANSWER

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)*

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__ ANURAG. __

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