Question

Find the ratio 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 midpoing of the segment is (4, 0), so the value of m is 0.

How to find m?

if point P divides the line segment AB, then P is the midpoint of said segment.

Remember that for two points (x₁, y₁) and (x₂, y₂) the midpoint is given by:

M = ( (x₂ + x₁)/2, (y₂ + y₁)/2)

Here we have the points (2, 3) and (6, -3), the midpoint will be:

( (2 + 6)/2, (3 - 3)/2)

(4, 0)

So the value of m must be zero.