Three vertices of a parallelogram abcd are a 2 3

Asked by admin @ 03/08/2021 in Math viewed by 302 People

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)

Answered by admin @ 03/08/2021

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….

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