Q. 31

# A quadrilateral has the vertices at the point (-4,2), (2,6), (8,5) and (9,-7). Show that the mid-point of the sides of this quadrilateral are the vertices of a parallelogram.

Let the vertices of quadrilateral be P(-4,2), Q(2,6), R(8,5) and S(9,-7)

Let A, B, C and D are the midpoints of PQ, QR, RS and SP respectively.

Now, since A is the midpoint of P(-4, 2) and Q(2, 6)

Coordinates of A are

Coordinates of B are

Coordinates of C are

and

Coordinates of D are

Now,

we find the distance between A and B

Now, since length of opposite sides of the quadrilateral formed by the midpoints of the given quadrilateral are equal .i.e.

AB = CD and AD = BC

it is a parallelogram

Hence Proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Some Interesting Proofs in Geometry36 mins
Section Formula30 mins
Previous Year RMO Questions43 mins
NCERT | Most Important Proofs for Boards28 mins
Know About Important Proofs in Triangles33 mins
Champ Quiz | Distance Formula30 mins
Set of Questions on Section Formula54 mins
Coordinate Geometry Important Questions38 mins
Measuring distance by Distance formula49 mins
Champ Quiz | Previous Year NTSE QuestionsFREE Class
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