Answer:
The value of m is 0.
Step-by-step explanation:
Let the point P divides the line AB in k:1.
The coordinates of line AB are A (2, 3) and B (6, -3).
The coordinates of P are (4,m).
By section formula, if a point divides a line in m:n, then
[tex]P=(\frac{x_2m+x_1n}{m+n},\frac{y_2m+y_1n}{m+n})[/tex]
[tex]4=\frac{6k+2}{k+1}[/tex]
[tex]4(k+1)=6k+2[/tex]
[tex]4k+4=6k+2[/tex]
[tex]2k=2[/tex]
[tex]k=1[/tex]
It means the point P divides the line AB in 1:1. So, P is the midpoint of AB.
[tex]m=\frac{3+(-3)}{2}=\frac{0}{2}=0[/tex]
Therefore the value of m is 0.