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1. Introduction to Coordinates
A coordinate system helps us describe the exact position
of a point. Instead of saying that an object is to the
left, right, above or below another object, we can use
numbers to identify its position precisely.
The coordinate plane is formed by two perpendicular number
lines. These are called the horizontal axis and vertical axis.
Coordinate:
A number used to describe the position of a point.
Practice Questions
Question 1
Why do we use a coordinate system?
A coordinate system helps us identify the exact position
of a point using numbers.
Question 2
What is a coordinate?
A coordinate is a number used to describe the position
of a point.
Question 3
What are the two axes used in a coordinate plane?
The horizontal x-axis and the vertical y-axis.
Question 4
Why are the two coordinate axes perpendicular to each other?
The perpendicular axes provide a clear two-dimensional
reference system for locating points horizontally and
vertically.
2. Coordinate Plane
The coordinate plane is a two-dimensional plane formed by
the intersection of two perpendicular axes.
The horizontal axis is called the x-axis and the vertical
axis is called the y-axis.
The point where the two axes intersect is called the origin.
Practice Questions
Question 5
What is the coordinate plane?
It is a two-dimensional plane formed by two perpendicular
coordinate axes.
Question 6
Which axis is horizontal?
The x-axis is horizontal.
Question 7
Which axis is vertical?
The y-axis is vertical.
Question 8
What are the coordinates of the origin?
3. Ordered Pairs
The position of a point is generally represented by an
ordered pair written in the form:
The first number gives the x-coordinate and the second
number gives the y-coordinate.
Important:
The order of the numbers matters.
For example, (2, 5) and (5, 2) represent different positions.
Practice Questions
Question 9
What is an ordered pair?
An ordered pair is a pair of numbers written in a specific
order, usually as (x, y), to represent the position of a point.
Question 10
In the ordered pair (7, 4), which number is the x-coordinate?
7 is the x-coordinate.
Question 11
In the ordered pair (7, 4), which number is the y-coordinate?
4 is the y-coordinate.
Question 12
Are (3, 5) and (5, 3) the same point?
No. Since the order of coordinates is different, they
represent different points.
4. Reading and Plotting Points
To plot a point, first move horizontally according to the
x-coordinate and then move vertically according to the
y-coordinate.
The signs of the coordinates indicate the direction in
which the point lies from the origin.
Positive x → right
Negative x → left
Positive y → up
Negative y → down
Practice Questions
Question 13
In which direction do we move when the x-coordinate is positive?
We move towards the right from the y-axis.
Question 14
In which direction do we move when the x-coordinate is negative?
We move towards the left.
Question 15
In which direction do we move when the y-coordinate is positive?
We move upward.
Question 16
In which direction do we move when the y-coordinate is negative?
We move downward.
5. Quadrants
The x-axis and y-axis divide the coordinate plane into four
regions called quadrants.
|
Quadrant
|
x-coordinate
|
y-coordinate
|
|
First
|
Positive
|
Positive
|
|
Second
|
Negative
|
Positive
|
|
Third
|
Negative
|
Negative
|
|
Fourth
|
Positive
|
Negative
|
Practice Questions
Question 17
What are the signs of the coordinates of a point in the
first quadrant?
Both x and y coordinates are positive.
Question 18
What are the signs of the coordinates of a point in the
second quadrant?
x is negative and y is positive.
Question 19
What are the signs of the coordinates of a point in the
third quadrant?
Both x and y are negative.
Question 20
What are the signs of the coordinates of a point in the
fourth quadrant?
x is positive and y is negative.