Question

13. If the point P, which divides the line segment joining (-1, 4) and (3, 7), lies on the line 4x
- 2y + k =0, then find the value of k.
equidistant from the points (3,4) and (6,7).​ pls urgent

Answer 1

Step-by-step explanation:

The eqn. of the line joining (-1,4) and (3,7) is 3x-4y+19=0.

Let the co-ordinates of P be (a,b).

Then it satisfies both the line :

3x-4y+19=0

4x-2y+k=0.

Thus, we get

3a-4b+19=0 .... ..... (i)

4a-2b+k=0 .... .... (ii)

Since (a,b) is equidistant from (3,4) and (6,7)

(a-3)^2 +(b-4)^2 = (a-6)^2+(b-7)^2

or a+b=10 ..... .... (iii)

Solving (i) & (iii), we get

a=3 & b=7.

Now, putting these values in (ii), we get

k= 2.