Question

Find the ratio in which P (4,m) divide the line segment jioing the points A(2,3) and B(6,-3) .find m

Answer 1

Using section formula i have solved this hope u may understand it

Answer 2

Answer:

The ratio it divides is 1:1

The value of 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 C in a ration k:1

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

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

Equating x-coordinate

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

$4k+4=2+6k$

$2k=2$

$k=1$

The ratio it divides is 1:1

Similarly,Equating y-coordinate and put k=1

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

$m=\frac{(3(1)-31)}{1+1}$

$m=\frac{0}{2}$

$m=0$

The value of m=0.