Section Formula CBSE NCERT Solutions Chapter 7 Exercise 7.2 Question 6
6. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order,
find x and y.
Solution:
Let A = (1,2), B = (4, y), C= (x, 6) and D= (3, 5)
We know that diagonals of parallelogram bisect each other. It means that coordinates of midpoint of diagonal AC would be same as coordinates of midpoint of diagonal BD. (1)
Using Section formula, the coordinates of midpoint of AC are:
Using Section formula, the coordinates of midpoint of BD are:
(
According to condition (1), we have
According to condition (1), we also have
Therefore,
and
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