Question

in a what ratio does point P on x axis divide the line segment joining point A(-4,5) B(3,-7).also find the coordinate of P

Answer 1

Let the given points be A (-4,5) , B (3,-7)
Let the x-axis cuts the line segment AB at point P in the ratio k:1
Then the coordinates of point P are
P [(m₁x₂+m₂x₁)/m₁+m₂ , (m₁y₂+m₂y₁)/m₁+m₂]
Here we have,
x₁ = -4 , y₁ = 5
x₂ = 3  , y₂ = -7
m₁ = k , m₂ = 1
So, coordinates of P are
P [ {(k)(3) + (1)(-4)}/k+1  ,   {(k)(-7) + (1)(5)}/k+1 ]
P [ 4k-4/k+1  ,   -7k+5/k+1 ]
Since P lies on x-axis, so its y coordinate must be zero.
 -7k+5/k+1= 0
-7k + 5 = 0
7k = 5
k = 5/7
Hence required ratio is k:1 = 5/7:1

Answer 2

Answer:

Let x-axis divides the line segment joining (–4, –6) and (–1, 7) at the point P in the ratio 1 : k.

Now, coordinates of point of division P are

x coordinate = (-1 - 4k) / (k + 1)

y coordinate = (7 - 6k) / (k + 1)

Since P lies on x-axis, therefore y coordinate = 0

(7 - 6k) / (k + 1) = 0

7 - 6k = 0

k = 7/6

Hence, the ratio is 1:7/6 = 6:7

Now, the coordinates of P are (-34/13, 0)