ANSWERS: 1
  • 1) "Cartesian coordinates in two dimensions: Choosing a Cartesian coordinate system for a plane means choosing an ordered pair of lines (axes) at right angles to each other, a single unit of length for both axes, and an orientation for each axis. The point where the axes meet is taken as the origin for both axes, thus turning each axis into a number line. Each coordinate of a point p is obtained by drawing a line through p perpendicular to the associated axis, finding the point q where that line meets the axis, and interpreting q as a number of that number line." "Generalizations One can generalize the concept of Cartesian coordinates to allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In those oblique coordinate systems the computations of distances and angles is more complicated than in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold." Source and further information: http://en.wikipedia.org/wiki/Y-axis 2) One usual application of a 2-dimensional Cartesian coordinates system with different units along each axis is the representation of the variation of a specific variable over time. In this case, the x-axis is time, and the y-axis is for the values of the variable.

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