Coordinate geometry- CBSE class 9

CONTENT LIST

Introduction

Coordinate geometry is a branch of mathematics that deals the relation between algebra and geometry by using graphs. With the concept of Coordinate geometry, We find the position of any point on the plane by using the ordered pairs.Nevgation tool,Google map works on this concept.

The Cartesian system

A system for describing the position of a point in a plane is known as the Cartesian system . A point in the plane is located by referring from two perpendicular lines in a Cartesian system. The horizontal line XX’ is called X-axis, and the vertical line YY’ is called Y-axis.The point of intersection of horizontal line XX’ and the vertical line YY’ is called orgine.
The part of X axis on RHS of origin is considered as positive x axis and the one towards left of origin is taken as the negative x axis. Similarly the part of y axis above the origin, is taken as the positive y axis and the part of y axis below the origin, is taken as the negative y axis.

Quadrants and Coordinate Axes

The plane is divided into four sections by the X and Y axes and each section is termed as quadrent. The quadrants are numbered I, II, III, and IV in anti-clockwise order from OX. The Cartesian plane, also called as the coordinate plane or the XY plane. These X,Y axes are also known as coordinate axes.

Quadrant-1:

In this quadrant, both coordinates of the point are positive.
P(+x,+y)

Quadrant-2:

In this quadrant, x− coordinate is negative, and y−coordinate is positive.
P(−x,+y)

Quadrant-3:

In this quadrant, x−coordinate is negative, and y−coordinate negative.
P(−x,−y)

Quadrant-4:

In this quadrant, x−coordinate is positive, and y−coordinate is negative.
P(+x,−y)

Using the coordinate axes, we describe any point in the plane with the help of an ordered pair of numbers. Example : Point A is represented by an ordered pair (x, y) where x is called as the abscissa (perpendicular distance from Y axis) and y is called the ordinate of the point (perpendicular distance from X axis).Every point in the coordinate plane is expressed by an ordered pair of x and y coordinates.

How to locate point (x,y) in cordinate plane?

Step1: Start at (0, 0),ie from the origin of the coordinate plane .
Step2: Move over x units on X-axis to the right or left.
step3: Move over y units on Y-axis up or down. Mark the point.

Example: Plot (3, 4) and (-7, 1) Points .

The ordered pair (3, 4) is in 1st quadrent and it is found, when you move 3 steps to the right on the x-axis and 4 steps upwards on the y-axis.
The ordered pair (-7, 1) is in 2nd quadrent and it is found,when you move 7 steps to the left on the x-axis and 1 step upwards on the y-axis.

Check your Understanding

Question: The horizontal line in the cartesian plane which determines the position of a point is called:
a. Origin
b. X-axis
c. Y-axis
d. Quadrants

Answer: b. X-axis

Question: The vertical line in the cartesian plane which determines the position of a point is called:
a. Origin
b. X-axis
c. Y-axis
d. Quadrants

Answer:c. Y-axis

Question: The point of intersection of horizontal and vertical lines determining the position of a point in a cartesian plane is called:
a. Origin
b. X-axis
c. Y-axis
d. Quadrants

Answer:a. Origin

Question: the coordinates of a point are (4, 0), then it lies in:
a. X-axis
b. Y-axis
c. At origin
d. Between x-axis and y-axis

Answer:b. Y-axis

Question: The coordinates of a point are (-3, 5), then it lies in:
a. First quadrant
b. Second quadrant
c. Third quadrant
d. Fourth quadrant

Answer:b. Second quadrant

Question: If y coordinate of a point is zero, then the point lies on:
a. First quadrant
b. Second quadrant
c. X-axis
d. Y-axis

Answer:c. X-axis

Related Topics

Linear Equation in Two Variables