if A(1,2),B(4,3),C6,6) are the three vertices of a parallelogram ABCD , find the coordinates of the fourth vertex?

Asked by sharmishtha rath | 15th Dec, 2013, 10:13: AM

Expert Answer:

Let (x, y) be the coordinates of the vertex D.
 
We know that the diagonals of a parallelogram bisect each other.
 
Let us now find the midpoint of the line joining A and C.
 
Therefore, the coordinates of the midpoint of AC are 
Similarly the coordinates of the midpoint of BD are 
By the property of the parallelogram, we have
 
 
 
Thus, the coordinates of the vertex D are D=(3,5)

Answered by Vimala Ramamurthy | 15th Dec, 2013, 12:37: PM

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