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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.

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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?
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APPEARS IN

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