Question

if A(-1,0), B (3, 1) and C (2,2) are verticas of a parallelogram
ABCD Then find the vertex of D.​

Answer 1

Answer:

Let the fourth vertex is D(x,y).

In a parallelogram ABCD,the diagonals

bisect each other i,e., Midpoints of the

diagonals are equal.

Midpoint of AC =Midpoint of BD

=> [(-1+2)/2 , (0+2)/2] = [(3+x)/2 , (1+y)/2] ,

=> [1/2 , 1] = [(3+x)/2 , (1+y)/2] ,

=> (3+x)/2 = 1/2,

=> (3+x) = 1,

=> x = -2

similarly,

(1+y)/2 = 1,

=> (1+y) = 2,

=> y = -1

therefore,

vertex D = (-2,-1).