Section Formula
Lesson · Beginner
Geometry: Coordinate Geometry
If
then
When m=n=1,
Thus, if A=(x_1,y_1) and B=(x_2,y_2), the midpoint is
If C is a fraction t of the way from A to B, then
or equivalently,
For 0 ≤ t ≤ 1, the point lies on the segment AB.
Points A=(-4,7), B=(11,-8), and P=(2,1) are collinear. Find AP:PB.
Use
From the x-coordinates,
so
Therefore P is 2/5 of the way from A to B, giving
Point P divides AB in the ratio AP:PB=2:3. Point Q divides PB in the ratio PQ:QB=1:2.
Express Q in terms of A and B.
First,
Since PQ:QB=1:2,
Substituting,
So