Question

In what ratio does the point p(p,-1) divide the line segment joining the points a(1,-3) and b(6,2)? Hence find the value of p

Answer 1

this is the solution for your question

Answer 2

P divide AB in the Ratio 2 : 3. Hence the value of p is 3.

Step-by-step explanation:

Let Point P ( p , -1 ) divides Segment AB in the ratio = m : n (say)

point A( x₁ , y₁) ≡ ( 1 , -3)  

point B( x₂ , y₂) ≡ (6 , 2)  

To Find:  

p ≡ ?

m : n = ?  

Solution:  

IF a Point P divides Segment AB internally in the ratio m : n, then the Coordinates of Point P is given by Section Formula as

$x=\frac{(mx_{2} +nx_{1}) }{(m+n)}\\ \\and\\\\y=\frac{(my_{2} +ny_{1}) }{(m+n)}$

Substituting the value y = -1 for y-coordinate we get

$-1=\dfrac{m(2) +n(-3) }{(m+n)}\\\\-m-n=2m-3n\\\\-m-2m=-3n+n\\\\-3m=-2n\\\\\dfrac{m}{n} =\dfrac{2}{3}$

Therefore P divide AB in the Ratio 2 : 3

Now for p we have

$p=\dfrac{2\times 6 +3\times 1 }{(2+3)}\\\\p=\dfrac{15}{5}=3\\\\p=3$

Hence the value of p is 3.