# If the points A (6, 1), B (8, 2), C (9, 4) and D (k, p) are the vertices of a parallelogram taken in order, then find the values of k and p.

Our given vertices are A(1, -2), B(3, 6) and C(5, 10) and fourth vertex be D(k, p)

It is given that quadrilateral joining these four vertices is parallelogram, ie □ABCD is parallelogram.

We know that diagonals of parallelogram bisect each other, ie midpoint of the diagonals coincide.

Let E(xm , ym) be the midpoint of diagonals AC and BD. By midpoint formula,

x = , y = For diagonal AC,

xm = , ym = xm = , ym = E(xm , ym) ≡ ( , )

For diagonal BD, = , = k = 15 – 8 , y = 5 – 2

k = 7 and p = 3

Hence, our fourth vertex is D(7 , 3)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Chemical Co-ordination VS Neural Co-ordination48 mins  Quiz | Chemical Co-ordination47 mins  Some Interesting Proofs in Geometry36 mins  Quiz | Neural Co-ordinataion51 mins  Section Formula30 mins  Previous Year RMO Questions43 mins  NCERT | Most Important Proofs for Boards28 mins  Know About Important Proofs in Triangles33 mins  Foundation | Human Endocrine System58 mins  Champ Quiz | Distance Formula30 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 