1. To locate the position of an object or a point in a plane, we require two perpendicular lines. One of them is horizontal, and the other is vertical.
2. The plane is called the Cartesian, or coordinate plane and the lines are called the coordinate axes.
3. The horizontal line is called the x -axis, and the vertical line is called the y - axis.
4. The coordinate axes divide the plane into four parts called quadrants.
5. The point of intersection of the axes is called the origin.
6. The distance of a point from the y - axis is called its x-coordinate, or abscissa, and the distance of the point from the x-axis is called its y-coordinate, or ordinate.
7. If the abscissa of a point is x and the ordinate is y, then (x, y) are called the coordinates of the point.
8. The coordinates of a point on the x-axis are of the form (x, 0) and that of the point on the y-axis are (0, y).
9. The coordinates of the origin are (0, 0).
10. The coordinates of a point are of the form (+ , +) in the first quadrant, (–, +) in the second quadrant, (–, –) in the third quadrant and (+, –) in the fourth quadrant, where + denotes a positive real number and – denotes a negative real number.
11. If x ≠ y, then (x, y) ≠ (y, x), and (x, y) = (y, x), if x = y.
The best example of coordinates in everyday life is use of longitude and latitude on globe. Each unique location on the earth has a unique combination of longitude and latitude. Global positioning system used by radio taxi operators also uses x,y coordinates to find exact location of a vehicle.
1.In which quadrant or on which axis do each of the points (– 2, 4), (3, – 1), (– 1, 0), (1, 2) and (– 3, – 5) lie? Verify your answer by locating them on the Cartesian plane.
Finding exact location of a point from the origin
This can be done by using formula, which looks complicated, and by using a graph paper. Suppose you need to calculate the following coordinates’ distance from origin: (-2,4).
Making a rough graphical representation will give you following figure:
Here you get a point where perpendiculars from x and y axes are intersecting, all you need to calculate is the length of dotted arrow, which is the length of the point from origin. This dotted line is diagonal of the rectangle formed by perpendiculars from x and y axes. So the required answer will be:
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