Answer :

We know that a quadrilateral is a parallelogram if the co-ordinates of mid-point s of its both the diagonals are same.

Therefore, we’ll find the mid-point s of diagonal AC and BD.


Let the co-ordinates of mid-point of AC be (x3, y3).


And, we know mid-point formula, i.e. the coordinates of mid-point of line joining (x1, y1) and (x2, y2) is




(Where, (x1, y1) and (x2, y2) are the coordinates of A and C




Co – ordinates of mid-point of AC =


Now, Let the co-ordinates of mid-point of BD be (x4, y4).


And, since it is a mid-point –



(Where, (x5, y5) and (x6, y6) are the coordinates of B and D.




Co – ordinates of mid-point of BD =


And, since these are equal –


ABCD is a parallelogram.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

The point s P andWest Bengal Mathematics

The co-ordinates West Bengal Mathematics

The co-ordinates West Bengal Mathematics

Find the co-ordinWest Bengal Mathematics

Let us calculate West Bengal Mathematics

If the point s (3West Bengal Mathematics

If (x1West Bengal Mathematics

The sides of rectWest Bengal Mathematics

C is the centre oWest Bengal Mathematics

If the point s P(West Bengal Mathematics