# 2.14: Points in a Coordinate Plane

**Basic**Created by: CK-12

**Practice**Points in the Coordinate Plane

A map of a neighborhood block shows the corner of Brown Street and Smith Street. There is a house on the map marked with a black dot. The coordinates of this house need to be plotted correctly for the City Planner.

In this concept, you will learn how to determine the coordinates of a point on a coordinate grid.

### Coordinate Grid

A **coordinate grid** is a graph used to locate points in space. A pair of numbers, called **coordinates**, tells where the point is in two-dimensional space.

Here is an example of a coordinate grid.

The horizontal axis, or the line that goes across side to side, is called the \begin{align*}x\end{align*}**axis**. The vertical axis, or the line that goes up and down, is called the \begin{align*}y\end{align*}**axis**. The point where the two axes meet is called the **origin .** The origin has the value of (0,0).

Every line on the \begin{align*}x\end{align*}

When a point has already been plotted on a coordinate grid, an ordered pair identifies its location. A coordinate is written in the form of an **ordered pair.** In an ordered pair, there are two numbers put inside a set of parentheses. The first number is an \begin{align*}x\end{align*}

Here is an example of an ordered pair:

(3, 4)

This ordered pair has two values. It has an \begin{align*}x\end{align*}

This ordered pair can be plotted on the coordinate grid.

To graph (3,4) on the grid, start at the origin and count three units on the \begin{align*}x\end{align*}

Sometimes, the ordered pair contains a zero, for example:

(0, 4)

This means that the \begin{align*}x\end{align*}

The point actually falls directly on the \begin{align*}y\end{align*}

### Examples

#### Example 1

Earlier, you were given a problem about the neighborhood map that shows a point of a house on the block. The city planner needs the coordinates of that house.

First, locate the point on the coordinate grid. There is only one point on this grid, so it is easy to identify.

Next, look at where that point is located on the \begin{align*}x\end{align*}

Then, look at where the point is located on the \begin{align*}y\end{align*}

The answer is (2,3). This is the coordinate pair for the house on the map.

#### Example 2

Graph (9,3) on the coordinate grid.

First, look at the \begin{align*}x\end{align*}

Next, look at the \begin{align*}y\end{align*}

Then, mark the coordinate pair on the grid with a dot.

The answer goes on (9, 3) where the dot is.

Use the coordinate grid to answer the following questions.

#### Example 3

What is the ordered pair for point A?

First, locate the point on the coordinate grid.

Next, follow down to the \begin{align*}x\end{align*}

Then, follow from the point over to the \begin{align*}y\end{align*}

The answer is (3,2)

#### Example 4

What is the ordered pair for point B?

First, locate the point on the coordinate grid.

Next, follow down to the \begin{align*}x\end{align*}

Then, follow from the point over to the \begin{align*}y\end{align*}

The answer is (4,6)

#### Example 5

What is the ordered pair for point C?

First, locate the point on the coordinate grid.

Next, follow down to the \begin{align*}x\end{align*}

Then, follow from the point over to the \begin{align*}y\end{align*}

The answer is (7,9)

### Review

Write the coordinates of each point.

1. A

2. B

3. C

4. D

5. E

6. F

7. G

8. H

9. I

10. J

11. K

12. L

Graph and label each point on the coordinate grid.

13. M(1, 3)

14. N(2, 4)

15. O(0, 6)

16. P(8, 6)

17. Q(2, 2)

18. R(4, 7)

19. S(7, 7)

20. T(9, 0)

21. U(4, 6)

22. V(0, 5)

23. W(6, 8)

24. Y(1, 7)

25. Z(3, 4)

### Answers for Review Problems

To see the Review answers, open this PDF file and look for section 2.14.

### Resources

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In this concept, you will learn how to determine the coordinates of a point on a coordinate grid.