Amateur Extra: Rectangular Coordinates

What do the two numbers represent that are used to define a point on a graph using rectangular coordinates? [E5C11]

A. The magnitude and phase of the point
B. The sine and cosine values
C. The coordinate values along the horizontal and vertical axes
D. The tangent and cotangent values

This might seem like a strange and really lame question, but I think the reason for it is to make sure you understand the difference between rectangular and polar coordinates.

In a rectangular coordinate system, the two numbers represent C. The coordinate values along the horizontal and vertical axes.  That might seem rather obvious.  For example, if you think of a checkerboard, for example, and measure over three squares, and up four, then those coordinates would be 3,4.

Polar coordinates on the other hand, are represented by a radius and an angle.  For example if you were to take a string and pin it to the center of the checkerboard, then rotate that string around the center, at a given length.  So if your string was 6″ long and it was at 90º from the horizontal, your polar coordinates would be 6∠90º.

See the image above for what this looks like.

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