Question

Find the radio in which P (4, m) divides the line segment joining the points A (2, 3) and B (6, -3). Hence find m

Answer 1

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

$P=(\frac{x_2m+x_1n}{m+n},\frac{y_2m+y_1n}{m+n})$

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

$4(k+1)=6k+2$

$4k+4=6k+2$

$2k=2$

$k=1$

It means the point P divides the line AB in 1:1. So, P is the midpoint of AB.

$m=\frac{3+(-3)}{2}=\frac{0}{2}=0$

Therefore the value of m is 0.