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How to Do Mathematics From Two Coordinates

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In geometry, a coordinate system is a system which gives numbers or coordinates to determine the exact location of point in a plane. In elementary math, the plane is simply in Real number system but in advanced mathematics it can be in complex plane. Before moving to solve problems, it is necessary to learn basic coordinates.


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    Polar coordinate system. Another common coordinate system for the plane is the Polar coordinate system. A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ. Then there is a unique point on this line whose signed distance from the origin is r for given number r. For a given pair of coordinates (r, θ) there is a single point.
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    Cylindrical and spherical coordinate systems. There are two common methods for extending the polar coordinate system to three dimensions. In the cylindrical coordinate system, a z-coordinate with the same meaning as in Cartesian coordinates is added to the r and θ polar coordinates. Spherical coordinates take this a step further by converting the pair of cylindrical coordinates (r, z) to polar coordinates (ρ, φ) giving a triple (ρ, θ, φ).
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    Geometry Of Problem. It depends on geometry of problem whether it can be solved by using two coordinate system or three. If it's a cylindrical or spherical figure,then it 'll surely have z-direction so 2 dimensions fails here. Two dimensional object problems can be solved within the Cartesian Graph system fairly readily.
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    The Distance Formula. This is a formula which is used to calculate distance between two points in a plane. For example, find the distance between the points (–2, –3) and (–4, 4)? Plug the coordinates into the Distance Formula:
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    Slope of a Straight Line.One of the most important properties of a straight line is in how it angles away from the horizontal. This concept is reflected in something called the "slope" of the line. Let's take a look at the straight line y = ( 2/3 )x – 4. To find the slope, we will need two points from the line. Pick two x's and solve for each corresponding y: If, say, x = 3, then y = ( 2/3 )(3) – 4 = 2 – 4 = –2. If, say, x = 9, then y = ( 2/3 )(9) – 4 = 6 – 4 = 2. (The x-values were picked to be multiples of three because of the fraction. It's not a rule that you have to do that, but it's a helpful technique.) So the two points (3, –2) and (9, 2) are on the line y = ( 2/3 )x – 4..

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  • Carefully, look at geometry of problem.
  • Redraw the figure in your rough work to understand it clearly.

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Categories: Coordinate Geometry

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