MS2013 Assignment – Test 1 Make-Up

Rectangles versus rhombuses

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2. Rectangles versus rhombuses:

Which properties do they have in common?

Which properties distinguish rhombuses from rectangles (and vice-versa?)

3. Application of parallelograms: Adding Vectors.

The forces acting on an object determine the direction in which the object will move. A force is represented by a vector, showing not only how large the force is, but also the direction in which it acts.

Each vector is given by two plane coordinates and . If two forces act on an object at the same time, then the direction in which the object will move will be given by the sum of the two vectors:

. The vector is defined in coordinates by: and

Here are the coordinates of the vector , and the coordinates of the vector

a) Explain the geometric significance of the coordinates of the point (What do they represent in the diagram below? How are coordinates of a point constructed in general?)

b) Use congruent triangles and the properties of parallelograms and rectangles to prove that

if and only if is a parallelogram.

c) Let be the midpoint of segment Write a formula for the coordinates of M in terms of the coordinates of A and B. Which property of a parallelogram is useful in deriving this formula?

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