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

The value of m is 0.

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=((x_2m+x_1n)/(m+n),(y_2m+y_1n)/(m+n))`

`4=(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=(3+(-3))/(2)=(0)/(2)=0`

Therefore the value of m is 0.