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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

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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. 

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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

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