The Coordinate System

Introduction:

What is a coordinate plane?

A coordinate plane is a two-dimensional surface formed by the intersection of two numbers at a point zero called the origin.

Coordinate grid:

A coordinate grid is a set of grid lines used to graph and name the locations of points in a plane. A grid has a horizontal line called X–axis and a vertical line called Y–axis that intersect at the origin.

Ordered pair:

An ordered pair is the pair of elements that exist in a particular order. It is a combination of X– coordinate and Y–coordinate, having two values written in a fixed order within parentheses.

X–coordinate:

The distance of the point along horizontal line from the origin is called X–coordinate or X–axis. The first number
in the coordinate points represent the X–coordinate.

Y–coordinate:

The distance of the point along vertical line from the origin is called Y–coordinate or Y–axis. The second number in the coordinate points represents the Y–coordinate.

Origin:

The point at which the X–axis and Y–axis intersect is called the origin.

What is quadrant?

A quadrant is the region in a coordinate plane obtained by the intersection of two axes. A quadrant has been divided into 4 regions.

• Quadrant I: x > 0, y > 0; (+,+)
• Quadrant II: x < 0, y > 0; (-,+)
• Quadrant III: x < 0, y < 0; (-,-)
• Quadrant IV: x > 0, y < 0; (+,-)

14.1.1 The coordinate system

How to locate a point on the coordinate plane?

The following steps explain how to locate a point on the coordinate plane:

Step 1: Mark the point.

Step 2: Place the point in the quadrant by identifying the signs of X and Y coordinates.

Step 3: Find the X–coordinate of the given point from the origin.

Step 4:  Find the Y–coordinate of the given point from the origin.

Example 1: Locate the point A with the coordinates (2,3) on the graph paper.

Solution:

We use the following grip to locate the coordinates (2,3).

Example 2: Use the below image to determine each position of a place on a map.

Solution:

From the given image, we can identify 11 places on the grid map. The X–axis represents alphabets and the Y–axis represents numbers.

Therefore, the coordinate pairs are:

1. Fire station – (A,6)
2. Zoo – (B,9)
3. Bus station – (C,1)
4. Worship center – (D,8)
5. Police station – (E,5)
6. Amusement Park – (F,2)
7. School – (F,10)
8. Government office – (G,8)
9. Library – (I,9)
10. Park – (I,7)
11. Market – (I,2).

Example 3: Write the ordered pairs for the points given in the grid.

Solution:

From the given grid, we can identify the ordered pairs for the given points as:

A = (0,0)

B = (3,2)

C = (1,4)

D = (5,3)

In the above points,

X–axis represents the first number and Y–axis represents the second number.

Example 4:

Name the point for the given ordered pairs and label the points on the grid.

(2,0), (3,5), (4,3), (0,3), (1,5).

Solution:

The given ordered pairs are named as A (2,0), B (3,5), C (4,3), D (0,3) and E (1,5).

The above points are labelled in the grid as shown below:

Exercise:

• Determine the position and the place of a black and white knight on the chess board.

• Name the objects in the grid and write the ordered pairs on the coordinates.

• Locate the following points on the grid.

A (2,5), B (4,7), C (5,8), D (0,0), E (6,5)

• Find the points on the coordinate axes using the following ordered pairs.

(4,0), (2,5), (1,6), (4,5), (6,5)

• Graph and label the following points on the coordinate plane.

(2,0), (3,5), (4,3), (0,3), (1,5)

• Identify the ordered pairs in the below grid.

• Write the ordered pairs corresponding to the given points in the grid.

• How many quadrants are there on the coordinate axes?
• Identify the ordered pairs on the coordinate axes.

• Identify the ordered pairs on the grid and name the point to each pair.

What have we learned:

• Understand coordinate plane and coordinate axes.
• Differentiate between X – coordinate and Y – coordinate.
• Locate points on the coordinate axes.
• Understand the meaning of the ordered pair.
• Plot the ordered pairs on the coordinate plane.
• Graph the ordered pairs on the grid.

Summary:

Coordinate plane:

A coordinate plane is a two-dimensional surface formed by intersection of two numbers at a point zero called the origin.

Coordinate grid:

A coordinate grid is a set of grid lines used to graph and name the locations of points in a plane. A grid has a horizontal line called X–axis and a vertical line called Y–axis intersect at the origin.

Ordered pair:

An ordered pair is the pair of elements that exist in a particular order. It is a combination of X– coordinate and Y–coordinate, having two values written in a fixed order within parentheses.

Origin:

The point at which the X–axis and Y–axis intersect is called the origin.