find the ratio in which the point c(p,1)divides the line segment joining the points A(-4,4)and B(6,-1).hence find the value of p

Let the required ratio be k: 1.

 

Using section formula, we have the coordinates of C as:

But the coordinates of C are given as (p, 1).

Thus, we have:

1 = -k+4/ k+1

k+1=-k+4

2k=3

k=3/2

 

Thus, the required ratio is 3: 2.

 

Now, comparing the x-coordinate, we have:

p = 6k-4/k+1

p = 6(3/2)-4/ (3/2)+1

p = 18-8/ 3+2

p = 10/ 5 = 2