# 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. - Mathematics

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.

#### Solution

Let ABCD be a parallelogram in which the coordinates of the vertices are A (6, 1); B (8, 2); C (9, 4) and D (k, p).

Since ABCD is a parallelogram, the diagonals bisect each other. Therefore the mid-point of the diagonals of the parallelogram will coincide.

In general to find the mid-point P(x,y) of two points A(x_1, y_1) and  B(x_2,y_2) we use section formula as,

P(x,y) = ((x_1 + x_2)/2","(y_1 + y_2)/2)

The mid-point of the diagonals of the parallelogram will coincide.

So,

Co-ordinate of mid-point o AC          = Co-ordinate of mid-point of BD

Therefore,

((6 + 9)/2, (4 + 1)/2) = ((k + 8)/2","(p + 2)/2))

Now equate the individual terms to get the unknown value. So,

(k + 8)/2 = 15/2

k = 7

Similarly,

(p + 2)/2 = 5/2

p = 3

Therefore, k = 7 and p = 3

Concept: Section Formula
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 6 Co-Ordinate Geometry
Exercise 6.3 | Q 55 | Page 31