Leapfrog with Vectors
Here's a geometrical investigation
Choose a starting point and three other points, called A, B, and C.
From the starting point, leapfrog over point A. By that, I mean land on the point P1 such that A is the midpoint of P1 and the starting point.
Then leapfrog from that point over B. Then C, A, B and C.
Where will you finish? Try drawing it out first, then use the diagram below.
Move the points around, then use the "Jumps" slider to show the jumps.
Challenge 1
Can you prove what you saw using vectors?
Hint: It can be proven using vectors , and
Challenge 2
Does this work in 3D as well?