Question

If (1,-3), (-2,-3),&(-2,2) are three vertices of a parallelogram taken in that order then fourth vextex is...... ?

Answer 1

Fourth vertex is (1,2)

Answer 2

let the required vertices be x1 and y1
we know that in a parallelogram ,diagnols bisect each other.
so mid point of each diagnol is the same.

let E be the mid point of diagnols.
E --- (x , y)
E (x) =1 +(-2)/2 = -1/2
E(y) = -3 +2/2 = -1/2

the vertices of the mid point = { -1/2 , -1/2 }

mid point of AC = midpoint of BD

so ,midpoint of BD  = { -1/2 , -1/2 }
E(x) = -2 + x1 /2
-1/2 = -2 + x1/2

denominator 2 gets cancelled.

-1 +2 =x1
1 = x1

E (y) = -3 + y1 /2
-1/2 = -3 + y1/2

again denominator 2 gets cancelled.

-1 + 3 = y1
2 = y1

thus, the vertices of the fourth side = {1 , 2 }



hope it helps!!!!