Students can go through AP 9th Class Maths Notes Chapter 3 Co-Ordinate Geometry to understand and remember the concepts easily.

## Class 9 Maths Chapter 3 Notes Co-Ordinate Geometry

In this chapter, we learn

- A popular branch of maths known as coordinate geometry.
- Works of Rene Descartes.
- Cartesian system – The system used for describing the position of a point in a plane.
- Horizontal line – (X-axis)
- Perpendicular line – (Y-axis)
- Common point of two axes → origin point.
- Four quadrants formed by two axes on a plane.

- The distance from Y-axis is called X-coordinate.
- The distance from X-axis is called Y-coordinate.
- In other words X-coordinate is called abscissa and Y-coordinate is called ordinate.
- Y-coordinate of a point on X-axis is zero, because it is at zero distance from X-axis.
- X-coordinate of a point on Y-axis is zero, because it is at zero distance from Y-axis.
- All the points on X-axis are in the form of (x, 0).
- All the points on Y-axis are in the form of (0, y).
- The coordinates of origin are (0, 0)
- The coordinates of a point in Q
_{1}are of the form (+, +). - The coordinates of a point in Q
_{2}are of the form (-, +). - The coordinates of a point in Q
_{3}are of the form (-, -). - The coordinates of a point in Q
_{4}are of the form (+, -). - (x, y) and (y, x) are two different points if x ≠ y.
- (x, y) and (y, x) are same if (x = y).
- (x, y) are co-ordinates of a point on a plane where x, y are real numbers.
- Plotting the point means showing place of particular (unique) point.
- Procedure of drawing V-T graph, time distance graph, etc., (two variable graphs).

→ Positive, negative directions of axes :

When two number lines are drawn perpendicularly (at the point zero) as shown in figure.

Then,

- XX’ the horizontal line is called X-axis.
- YY’ the vertical line is called Y-axis.
- The intersecting point ‘O’ is called origin.
- The \(\overrightarrow{\mathrm{OX}}\) is called positive X-axis.
- The \(\overrightarrow{\mathrm{OX’}}\) is called negative X-axis.
- The \(\overrightarrow{\mathrm{OY}}\) is called positive Y-axis.
- The \(\overrightarrow{\mathrm{OY’}}\) is called negative Y-axis.

Quadrants :

→ First quadrant : The region in between X^{+} and Y^{+} axes is called first quadrant. Hence the co-ordinates of the points lie in first quadrant are in (+, +) format.

→ Second quadrant : The region in between (X^{–}) axis and (Y^{+}) axis is called second quadrant. Hence the co-ordinates of the points lie in second quadrant are in the format of (-, +) denoted by (Q_{2}).

→ Third quadrant : The region in between (X^{–}) axis and (Y^{–}) axis is called third quadrant and denoted by (Q_{3}). The coordinates of the points lie in third quadrant are in the format of (-, -).

Fourth quadrant: The region in between (X^{+}) axis and (Y^{–}) axis is called fourth quadrant and is denoted by (Q_{4}) The coordinates of the points lie in fourth quadrant are in the format of (+, -).

Examples of co-ordinates in quadrantwise

Q_{1} → (1, 1) (1, 5) (2, 7) (2.5, 3.2) (8, 9)…… etc.

Q_{2} → (-1,1) (-2, 3) (-3, 8), (-10, 1) …… etc.

Q_{3} → (-1, -1) (-4, -7) (-10, -100), (-10000, -1) …… etc.

Q_{4} → (1, -8) (2, -10) (3.7, -4.9) (7, -70) …… etc.

and Y – coordinates of points on X-axis are zero they are in the format of (a, 0).

For example, (-8, 0) (6, 0) (-7, 0) (-1, 0) (-2.5, 0) …….. etc are points on X-axis.

and X – coordinates of points on Y-axis are zero, they are in the format of (0, a), ‘a’ is real number.

For example, (0, √3 ) (0, -4) (0, 3√2 ) (0, -7) ……… etc.

The plane having all four quadrants is called cartesian plane (or) XY-plane (or) Coordinate plane in which both X, Y axes are inclusive. So X, Y axes and Q_{1}, Q_{2}, Q_{3}, Q_{4} together are called Cartesian/ XY/Coordinate plane.

Coordinates are nothing but the perpendicular distances from axes.

For example, X-coordinate is perpendi-cular distance from Y-axis and Y- coordinate is perpendicular distance from X-axis.

→ Steps for plotting a point in the plane (if co-ordinates are given) :

- Draw two perpendicular lines.
- Label thkrn as follows :

i) Intersection point ‘O’.

ii) Horizontal line X-axis.

iii) Perpendicular line Y-axis. - Choose a suitable scale like 1 cm = 1 unit.
- Mark 1, 2, 3, …….. (as per scale taken) on both axes.
- While marking consider positive values on X
^{+}, Y^{+}axes and negative values on X^{–}, Y^{–}axes. - Then draw perpendicular lines from the co-ordinates (of both axes). The inter-section of these two perpendiculars will be the position of given point.