Vectors in proof and problem solving
Solve the balance point of weighted points, a geometric proof with vectors (the line joining the midpoints of two sides of a triangle) and problems about speed and parallelograms by drawing vectors.
- سوريا: الصف ١٠
- أوكرانيا: الصف ٩
- روسيا: الصف ٩
- بريطانيا: السنة ١١
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الدليل
This extra studio is for students who can add vectors and multiply a vector by a scalar. The barycentre (weighted centre) of points A and B with weights 1 and 2 is the point G with OG = a + ٢b٣: G is nearer the point with more weight.
In a proof with vectors we write every segment as a vector and simplify with addition and scalar multiples. For example, in a triangle the segment joining the midpoints of two sides is parallel to the third side and half as long.
Common mistakes: taking the midpoint instead of the weighted point, forgetting to halve, and adding lengths instead of components.