# If (x1

A(x1, y1), B(x2, y2), C(x3, y3) and D(x4, y4)

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 (x0, y0).

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

Similarly, let the co-ordinates of mid-point of AC be (x5, y5).

And, since it is a mid-point –

Now, since ABCD is a parallelogram –

(x0, y0) = (x5, y5)

x0 = x5 and y0 = y5

x1 + x3 = x2 + x4 and y1 + y3 = y2 + y4

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
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

The sides of rectWest Bengal Mathematics

Let us calculate West Bengal Mathematics

The abscissa at tWest Bengal Mathematics

The mid-point of West Bengal Mathematics

If the point s (3West Bengal Mathematics

If (x1West Bengal Mathematics