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Co-ordinate Geometry

Coordinate geometry in scientific experiments Coordinate geometry in scientific experiments Coordinate geometry is mostly used by the scientists to analyze the results of experimental data. In scientific experiments, data collected for the independent and dependent variables is usually plotted on a graph. This graph uses Cartesian coordinates. On the x–axis, independent variable is plotted whereas on y–axis, dependent variable is plotted. By examining and analyzing the patterns on a graph, scientists can easily draw conclusions about the relationship between two variables.

Cartesian Plane

In 1637, Rene Descartes (1596 – 1650), a French mathematician introduced a system called the Cartesian coordinate system by providing the first systematic link between Euclidean geometry and algebra. A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane called Cartesian plane.

The Cartesian plane is formed by using two directed real number lines intersecting at right angles, as shown in below figure. Each directed line is called a coordinate axis. The horizontal directed line is called the x–axis and the vertical directed line is called the y–axis. The point of intersection of these two axes is called the origin and is denoted by the letter ‘O’.

















Each point in the Cartesian plane corresponds to an ordered pair (x, y) of real numbers x and y, called coordinates of the point. The x–coordinate, also known as abscissa, represents the directed distance from the y–axis to the point and the y–coordinate, also known as ordinate, represents the directed distance from the x–axis to the point, as shown in above figure.

Use of quadrants Use of quadrants The use of quadrants is important to map our vast and immense galaxy. Astronomers have divided it into different galactic quadrants, such as first, second, third and fourth.
Quadrants

The x and y axes divide the Cartesian plane into four regions called quadrants. Each of the four quadrants is designated by a Roman numeral, I, II, III, or IV. Quadrant I contains all coordinates with positive x and positive y values (+, +); Quadrant II contains all coordinates with negative x and positive y values (−, +); Quadrant III contains all coordinates with negative x and negative y values (−, −); and Quadrant IV contains all coordinates with positive x and negative y values (+, −).

Angles in Quadrants

Various types of angles were discussed earlier: acute angle, right angle, obtuse angle, straight angle, reflex angle and complete angle. Let us know where these angles lie w.r.t. quadrants.

Consider initial ray of the angle as the positive direction of the x-axis. The table below and the adjacent figure show in which quadrant the terminal ray is located.

S.No. Type of angle Measure of an angle Terminal ray position
1 Acute angle 0° < θ < 90° I quadrant
2 Right angle θ = 90° On the positive y-axis
3 Obtuse angle 90° < θ < 180° II quadrant
4 Straight angle θ = 180° On the negative x-axis
5 Reflex angle 180° < θ < 360° III and IV quadrants
6 Complete angle θ = 360° On the positive x-axis,
coinciding with terminal ray

Note: If the terminal ray of an angle lies on the axes (such as 0°, 90°, 180°, 270°, 360°), it is called a quadrantal angle.

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