Points In
Between Problem1 Point A is (0 , 10), and point B is (6 , 2) Find the coordinates of the point M, which is the midpoint of the line AB. Point P is on AB, but twice as close
to A as to B. Find the coordinates of P. A New TrickA ‘weighted’ average of two values, or points, works just like a normal (mean) average, except that it takes more of one value than the other… So, a ‘normal’ average of A and B would be:  which gives the midpoint of AB. Whereas a ‘weighted’ average of the points A and B, giving twice as much weight to A as to B, would be:
These should agree with your answers! Problem 2The points A and B, taken with the origin C (0, 0), make a triangle. Something rather surprising happens in any triangle, and you’re going to use these ‘weighted’ averages to see what… You’ve already found the midpoint of AB – namely M (3, 6). Now find the midpoints of the other two sides  N on CB, and P on CA. Now find the point G1, which is on AN, but twice as close to N as to A. Repeat this approach, to find the point G2, on BP, but twice as close to P as to B. And now find G3, on CM, but twice as close to M as to C. What did you discover? These three lines, joining each vertex of a triangle to its opposite midpoint, always cross at a single point inside the triangle – twothirds of the way from each vertex. The three lines are called the Medians,
and the special point is called the ‘Centroid’. ‘Mazin’ It works for any triangle you can think of. Try one of your own. Open the File as a Word Document

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