Respuesta :

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.

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