Point in between
Find the point on the line segment AB that is twice as far from B as it is from A.
Age
11 to 14
Challenge level
Problem
A has coordinates (0,10), and B has coordinates (6,2).
P is on the line segment AB.
The distance from P to A is half the distance from P to B.
Find the coordinates of P.
Student Solutions
The line segment AB can be split into 3 equal parts, as shown below.
Image
Image
So the point P is $2$ to the left of A, and $2\frac{2}{3}$ down from A, at $(2,7\frac{1}{3}).$