Question

Find the ratio in which p(4,m) divides the line segment joining the points A (2,3) and B (6,-3) hence find M

Answer 1

Let the point P(4,m ) divide’s the line segment joining the points A(2,3) & B(6,-3) in the ratio k : 1.
Here, x1= 2, y1= 3 , x2= 6 ,y2= -3 , x = 4 ,y = m, m1 = k , m2= 1
By using section formula :
The coordinates of the point P are :
P(x,y ) = P(m1x2 + m2x1/ m1+m2 , m1y2 + m2y1/m1 + m2)
(4,m ) = (k ×6 + 1×2/k+1 , k×-3 + 1×3/k+1)
(4,m) = (6k + 2/k+1, -3k +3/k+1).........(1)
On equating x coordinate both sides of eq 1,
4 = 6k + 2/k+1
4(k+1) = 6k+2
4k + 4 = 6k +2
4k -6k = 2 -4
-2k = -2
2k = 2
k = 2/2= 1
k = 1

On equating y coordinate both sides of eq 1,
m = -3k +3/k+1
m = -3(1) + 3 / 1+1 [k=1]
m = -3 +3 /2 = 0/2 = 0
m = 0
Hence, the the point P(4,m ) divide’s the line segment joining the points A(2,3) & B(6,-3) in the ratio 1 : 1. & m= 0.

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