# 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:

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

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