# Prove that the point (4,8), (0,2), (3,0) and (7,6) are the vertices of a rectangle.

Note that to show that a quadrilateral is a rectangle, it is sufficient to show that

(a) ABCD is a parallelogram, i.e., AC and BD bisect each other and,

(b) the diagonal AC and BD are equal Let A(4, 8), B(0, 2), C(3, 0) and D(7, 6) are the vertices of a rectangle.

Coordinates of the midpoint of AC are Coordinates of the midpoint of BD are Thus, AC and BD have the same midpoint.

Hence, ABCD is a parallelogram

Now, check for the diagonals by using the distance formula

AC = √(3 – 4)2 + (0 – 8)2

= √(-1)2 + (-8)2

= √1 + 64

= √65 units

and

BD = √(7 - 0)2 + (6 – 2)2

BD = √(7)2 + (4)2

BD = √49 + 16

BD = √65 units

AC = BD

Hence, ABCD is a rectangle.

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  Measuring distance by Distance formula49 mins  Champ Quiz | Previous Year NTSE QuestionsFREE Class  Coordinate Geometry Important Questions38 mins
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 