Question

Find the fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3),B(6,7),and C(8,3)

Answer 1

Answer:

Explanation:Let the fourth vertex be D (a,b)

Midpoint of AC = Midpoint of BD

[(-2+8) / 2 , (3+3) /2] = [(6 +a) / 2 , (7+b) /2]

[By Midpoint formula: x,y = [( x1+x2) / 2 ,(y1 +y2)/2]

[ 6/2 , 6/2] =  [(6 +a) / 2 , (7+b) /2]

6/2 =  (6 +a) / 2  and 6/2 = (7+b) /2

6 = 6 +a  and 6 = 7 + b

6 -6= a  and 6 -7 = b

a = 0  and b = -1

Hence , the fourth vertex is D ( 0, -1)