Question

find the ratio in which P(4,m) divide the line segment join the point A(2,3) and B(6,-3).Hence find m

Answer 1

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Answer 2

Answer:

m=0

Step-by-step explanation:

Given:  Point $P(x_3,y_3)=(4,m)$ divides the join of point $A(x_1,y_1)=(2,3)$ and point $B(x_2,y_2)=(6,-3)$  

To find : The value of m

Let the line AB divides by Point P in a ration k:1

Then, Using section formula $(x_3,y_3)=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}$

$P(4,m)=(\frac{6k+2}{k+1}),(\frac{-3k+3}{k+1})$

$x_3=\frac{x_1n+x_2m}{m+n}$

which means,

$4=\frac{6k+2}{k+1}$

$4k+4=6k+2\\-2k=-2\\k=1$

Hence, P is the mid point

$m=\frac{-3k+3}{k+1}$

k=1

$m=\frac{-3(1)+3}{1+1}$

$m=0$

Therefore, m=0