# Find the Ratio in Which the Point P(M, 6) Divides the Join of A(-4, 3) and B(2, 8) Also, Find the Value of M. - Mathematics

Find the ratio in which the point P(m, 6) divides the join of A(-4, 3) and B(2, 8) Also, find the value of m.

#### Solution

Let the point  P(m,6)  divide the line AB in the ratio  k :.1

Then, by the section formula:

x = (mx_2+nx_1)/(m+n) , y =(my_2+ny_1)/(m+n)

The coordinates of P are (m,6).

m = (2k-4)/(k+1) , 6 = (8k+3)/(k+1)

⇒ m (k+1)= 2k-4,6k+6=8k+3

⇒m (k+1) = 2k -4 , 6-3= 8k-6k

⇒m(k+1) = 2k-4, 2k = 3

⇒m(k+1) = 2k-4,k=3/2

Therefore, the point P divides the line AB in the ratio 3:2

Now, putting the value of k in the equation  m(k+1) = 2k-4 , we get:

m(3/2+1) = 2(3/2)-4

⇒  m((3+2)/2) = 3-4
 ⇒ (5m)/2 = -1 ⇒ 5m = -2 ⇒m=-2/5

Therefore, the value of m = -2/5

So, the coordinates of P are (-2/5,6).

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 15