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Cartesian Coordinate Distance Calculator

This calculator requires the use of Javascript enabled and capable browsers. This script determines the distance from one point on a plane to another point. This system for representing points by pairs of numbers is called a Cartesian coordinate system (sometimes called a rectangular coordinate system), named after the French philosopher and mathematician, Rene Descartes. The foundations of Cartesian Geometry are credited to him, of which this is a pillar. The plane grid is established by two perpendicular lines called axes; a graphic representation example is below the calculator. The horizontal line is called the horizontal axis, also known as the x-axis, as we have designated it. The vertical line is called the vertical axis and is designated the y-axis. The ordered pair of numbers (x, y) designating a point are called the coordinates of the point. The first element of the pair is called the first coordinate, the x-coordinate or the abscissa; the second element of the pair is called the second coordinate, the y-coordinate or the ordinate. The point where the axes cross is called the origin. The origin has coordinates (0, 0), which are the default conditions in our calculator. The coordinate is determined by a direct relationship to the number of equally spaced units along the vertical and horizontal axes. The axes separate the plane into four sections called quadrants. The upper right quadrant is called the first quadrant, the upper left quadrant is called the second quadrant, the lower left quadrant is called the third quadrant, and the lower right quadrant is called the fourth quadrant. The designations are in a counter-clockwise direction with each quadrant being a quarter of an hour on a conventional clockface. By definition, distances along the horizontal axis and to the right of the vertical axis are positive, distances along the horizontal axis to the left of the vertical axis are negative. Also by definition, distances along the vertical axis and above the horizontal axis are positive, distances along the vertical axis below the horizontal axis are negative. Thus there are two quadrants that are mixed with one coordinate positive and one negative, one that have both coordinates negative, and one that has both coordinates positive. By way of those definitions, a coordinate designation point can consist of both positive, both negative or a combination of positive and negative factors.

In our example, the arrows on the axes indicate that they extend infinitely in that direction. The intersection of the two x-y axes creates four quadrants indicated by the Roman numerals I, II, III, and IV. By definition, the quadrants are labeled counter-clockwise starting from the upper right quadrant. In quadrant I the values are both positive, (x,y), in quadrant II, they are mixed, (-x,y), in quadrant III, they are both negative, (-x,-y), and in quadrant IV, they are mixed, (x,-y). Point P is in quadrant I, at coordinates (5,2).

Enter a coordinate pair for each the starting and ending points according to the Cartesian coordinate system. Then click on "Calculate". The calculator will determine the straight line distance between the two points as well as present the coordinates of each point as entered in the standard designation.

Unit
Number
Required Data Entry
xA abscissa
yA ordinate
xB abscissa
yB ordinate
   
Calculated Results
Point A Coordinates
Point B Coordinates
Resulting Distance
Rounded Resulting Distance
Updated 8.13.11


Quadrant x values y values
I > 0 > 0
II < 0 > 0
III < 0 < 0
IV > 0 < 0


X-Y Axis


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