3. 1. Introduction to Coordinate Geometry:
What is a Geometry?The Branch of Mathematics Concerned with the properties
of and relationship between points, lines, planes, and figures
What is coordinate?
A pair of numbers that describe the position of a point
on a coordinate plane by using the horizontal and vertical
distances from the two reference axes.
Usually represented by (x,y) the x-value and y-value.
And O is the centre i.e (0,0) called origin.
What is Coordinate Geometry?
A coordinate geometry is a branch of
where the position of the points on the
plane is defined with the help of an
ordered pair of numbers also known as
The father of coordinate geometry was René Descartes
4. What is a Quadrants ?
Quadrant is the region enclosed by
the intersection of the X-axis and the
On the cartesian plane when the two
X-axis and Y-axis, intersect with each
other at 90º there are four regions
formed around it, and those regions
are called quadrants. So, every plane
has four quadrants each bounded by
half of the axes. Each quadrant is
denoted by Roman numerals and
named as Quadrant I, Quadrant II,
Quadrant III, and Quadrant IV based
on their position with respect to the
Definition: A quadrant can be
defined as a region/part of a
cartesian plane which is obtained
when the two axes intersect each
other. It is used to determine the
position of a point in a plane.
5. How do you represent the points on the XY-Plane?
For Example -1
Write the coordinates of each of the points P,Q,R,S,T and O from the figure?
The coordinates of the points P,Q,R,S,T
R=(-2,-3) S=(2,1) T=(4,-2)
6. 2. Points A(5,3) , B(-2,3) and D(5,-4) are the three vertices of a rectangle ABCD.
Plot these points on a graph paper and hence find the coordinates of the vertex C.
8. EXERCISE 3.1
1. How will you describe the position of a table lamp on your study table to another pers
Lamp on Table
Fist Draw a x and y line and mark the points and measure the
from x and y axis the distance of the lamp from y-axis is 30 cm and
x-axis 25 cm
11. 2.Cartesian System/Cartesian Coordinate System :
What is Cartesian
A Cartesian system is
the one which specifies
a point plotted uniquely
on a plane by a pair of
having a pre-defined
distance from the two
in the same unit of
12. Cartesian Plane: What is a Plane?
Flat surface that extends infinitely along length and width.
Cartesian is two dimensional grid
formed by drawing two number
One is perpendicular to each
other. i. e X- By horizontal and Y-
By Vertical and two point intersect
Then What is Cartesian Plane?
13. Abscissa and ordinate:
In the coordinate system, the term
refers to the y -coordinate in (x, y). In short,
the distance along the y-axis is called the
There is a difference in two terms
called coordinate and ordinate. The term
represents the position of the point along
arc and so on, whereas the term “ordinate”
represents the value of a coordinate on the
The ordinate is the second component of
an ordered pair. For example, if (x, y) is an
ordered pair, then y is the ordinate here. An
ordered pair is used to denote a point in the
Cartesian plane. It is the second of the two
terms (x, y) by which a point is defined, in a
system of fixed Cartesian Coordinate
plane. The first coordinate (x), in the plane,
is called the abscissa. The Cartesian
system designates each point in the XY
plane, uniquely, by a pair of numerical
A Is the Coordinate
14. What Is a Cartesian Coordinate Plane?
A Cartesian coordinate plane is a system of two perpendicular number lines on
which we locate points.
The Cartesian coordinate plane consists of two perpendicular lines, x-axis and
The horizontal line is called the x-axis.
The vertical line is called the y-axis.
The intersection point of these two axes is called origin and is represented
The axes split through the origin, which is marked as 0 on the graph.
The side on the right of 0 is positive, while everything on the left is negative.
Similarly, as you go higher, the numbers are positive, while the negative
numbers are written below 0
The positive x-axis has positive numbers such as 1, 2, 3, 4,…..
The negative x-axis has negative numbers such as -1, -2, -3, -4,…..
The positive y-axis has positive numbers such as 1, 2, 3, 4,…..
The negative y-axis has positive numbers such as -1, -2, -3, -4,…..
A Cartesian coordinate plane can simply be called a coordinate plane or a
It represents a 2-dimensional (2D) plane.
15. Example1: William wants to throw a ball into a bucket which is placed on the
coordinates (3, 10).
If William is standing on the coordinates (3, 5), how far will he have to throw the
To calculate how far William will have to throw the ball, we need to calculate the
distance between William and the bucket. The x-coordinate of William's location
and the bucket is 3
Thus, they are on a line parallel to the y-axis.
Hence, the distance between William and the bucket can be calculated as the
difference of the y-coordinates of both the points. 10−5=5units
Thus, Willam has to throw the Ball 5 unit w
16. ∴ a=3
We know that both the points P and Q lie on a line parallel to the x-axis, thus, their y-
coordinates are the same.
Example2: If point P (3,4) and point Q (5,7−a) lie on a line parallel to the x-
axis, then what is the value of a?
Example3: Jacob and Ethan want to make a frame using the
coordinates (1,2),(3,2),(3,0),(1,0).Based on the coordinates, Jacob says that the
frame will be a square while Ethan says that the frame will be a parallelogram. Can
you identify who is right?
We need to draw the above coordinates on a Cartesian plane to check the
shape they will form.
We can clearly see that the figure thus obtained is
square as all the four sides are equal and all the
four interior angles are 90∘
There fore, Jocob is right.
17. 3. Plotting a Point in the Plane if its Coordinate are Given
A point in a plane contains two components where order matters!
It comes in the form (x,y) where x comes first, and y comes second.
The x-value tells how the point moves
either to the right or left along the x-
This axis is the main
horizontal line of the rectangular
axis or Cartesian plane.
The y-value tells how the point
moves either up or down along the y-
This axis is the main vertical line of
the rectangular axis or Cartesian plane.
The numbers on a coordinate grid are used to locate points.
Each point can be identified by an ordered pair of numbers; that is,
a number on the x-axis called an x-coordinate, and a number
on the y-axis called a y-coordinate. Ordered pairs are written in parentheses