# If the Mid-point of the Line Joining (3, 4) and (K, 7) is (X, Y) and 2x + 2y + 1 = 0 Find the Value of K. - Mathematics

If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of k.

#### Solution

We have two points A (3, 4) and B (k, 7) such that its mid-point is P(x,y).

It is also given that point P lies on a line whose equation is

2x + 2y+ 1 = 0

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)

Therefore mid-point P of side AB can be written as

P(x,y) = ((k + 3)/2, (7 + 4)/2)

Now equate the individual terms to get,

x= (k + 3)/2

y = 11/2

Since, P lies on the given line. So,

2x + 2y + 1 = 0

Put the values of co-ordinates of point P in the equation of line to get,

2((k + 3))/2+2(11/2) + 1 = 0

On further simplification we get,

k + 15 = 0

So, k = -15

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 6 Co-Ordinate Geometry
Exercise 6.3 | Q 12 | Page 29