Points In
Between Problem1 Point A is (0 , 10), and point B is (6 , 2) Find the co-ordinates of the point M, which is the mid-point of the line AB. Point P is on AB, but twice as close
to A as to B. Find the co-ordinates 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 mid-point 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 mid-point of AB � namely M (3, 6). Now find the mid-points 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 mid-point, always cross at a single point inside the triangle � two-thirds 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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