**Important Concepts and Formulas**

**Coordinate Geometry**

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 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 if x = y, then (x, y) = (y, x).

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