Question

Three vertices of a parallelogram ABCD are A(-2,3), B (6,7), C(8,3). Find the fourth vertex D.
(Class 10 Maths Sample Question Paper)

Answer 1

SOLUTION:

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).

HOPE THIS WILL HELP YOU….

Answer 2

Hope it will help you

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

THERFORE,Fourth vertex is D ( 0, -1).