A Point Between an Interval
The coordinates of a point P that divides the interval between points and in the ratio m:n respectively are given by:
If the point P divides the interval externally in the ratio m:n, then the ratio is negative and P lies outside AB.
1. Divide AB into the ratio 3:4 where A is (6 -2) and B is (-7, 5).
2. If A is (-2, -1) and B is (1, 5), find the coordinates of the point P that divides AB externally in the ratio 2:5.
Extension: Angle Between 2 Curves
To measure the angle between two curves, measure the angle between the tangents to the curves at that point.
where and are the gradients of the tangents to the curves at the point of intersection.
Find the acute angle formed at the intersection of the curves and .