VectorsVectors
Before doing this exercise you should do the exercises under "Vectors" here.
Exercise
- Input a slider n taking on values ≥1.
- Input an equilateral triangle through the points A, B and C.
- Let the point A1 divide the segment BC in ratio 1:n. Input vectors and construct this:
When n=1 the segment between the points A and A1 is called a median. There are three medians in a triangle; use vectors to show that the three medians always intersect at one point, even if the triangle is not equilateral. The point of intersection is the centre of mass.
When n>1 a smaller triangle is formed inside the original triangle, as in the construction above. Make a conjecture about the smaller triangle! Prove your conjecture!
