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प्रश्न
Find the ratio in which the pint (-3, k) divide the join of A(-5, -4) and B(-2, 3),Also, find the value of k.
उत्तर
Let the point P (-3, k) divide the line AB in the ratio s : 1
Then, by the section formula :
`x = (mx_1 + nx_1) /(m+n) , y= (my_2 +ny_1)/(m+n)`
The coordinates of P are (-3,k).
`-3=(-2s-5)/(s+1) , k =(3s-4)/(s+1)`
⇒-3s-3=-2s-5,k(s+1)=3s-4
⇒-3s+2s=-5+3,k(s+1) = 3s-4
⇒-s=-2,k(s+1)= 3s-4
⇒ s =2,k(s+1)=3s-4
Therefore, the point P divides the line AB in the ratio 2 : 1.
Now, putting the value of s in the equation k(s+1)=3s-4 , we get:
k(2+1)=3(2)-4
⇒ 3k=6-4
⇒ 3k = 2⇒k=`2/3`
Therefore, the value of k`= 2/3`
That is, the coordinates of P are `(-3,2/3)`
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