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Points in the Coordinate Plane

Graph points on an x/y graph

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Points in the Coordinate Plane

Let's Think About It

License: CC BY-NC 3.0

A map of a neighborhood block in a town 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.

Guidance

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

Here is an example of a coordinate grid.

License: CC BY-NC 3.0

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*} axis has a different value. The values start at 0 at the origin and continue on the horizontal axis. Each line has a value of 1. Every line on the \begin{align*}y\end{align*} axis has a different value. The values start at 0 with the origin and continue on the vertical axis. Each line has a value of 1.

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*} value and the second number is a \begin{align*}y\end{align*} value \begin{align*}(x, y)\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*} value of 3 because the \begin{align*}x\end{align*} value comes first. It has a \begin{align*}y\end{align*} value of 4. Each ordered pair represents one point on a coordinate grid.

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*} axis first. Then working from the 3, count up four since the \begin{align*}y\end{align*} coordinate is four. That is where the point is plotted.

License: CC BY-NC 3.0

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

(0, 4)

This means that the \begin{align*}x\end{align*} value is zero, so you don’t move along the \begin{align*}x\end{align*} axis for your first point, instead you start counting up at zero. The \begin{align*}y\end{align*} value is four, so you count up four units from zero.

License: CC BY-NC 3.0

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

Guided Practice

Graph (9,3) on the coordinate grid.

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First, look at the x value in the ordered pair. The value is 9. This is the value on the horizontal axis. Starting at the origin, count across the horizontal axis to 9.

Next, look at the y value. The value is 3. Starting at the 9 on the x-axis, count up 3 units.

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

License: CC BY-NC 3.0

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

Examples

Use the coordinate grid to answer the following questions.

License: CC BY-NC 3.0

Example 1

What is the ordered pair for point A?

First, locate the point on the coordinate grid.

Next, follow down to the x-axis and write down the X value in the ordered pair.

Then, follow from the point over to the y-axis and write down the Y value in the ordered pair.

The answer is (3,2)

Example 2

What is the ordered pair for point B?

First, locate the point on the coordinate grid.

Next, follow down to the x-axis and write down the X value in the ordered pair.

Then, follow from the point over to the y-axis and write down the Y value in the ordered pair.

The answer is (4,6)

Example 3

What is the ordered pair for point C?

First, locate the point on the coordinate grid.

Next, follow down to the x-axis and write down the X value in the ordered pair.

Then, follow from the point over to the y-axis and write down the Y value in the ordered pair.

The answer is (7,9)

Follow Up

License: CC BY-NC 3.0

Remember the neighborhood map that shows a point of a house on the block? The city planner needs the coordinates of that house. 

License: CC BY-NC 3.0

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 x-axis. This map does not label values on each axis, so you will have to count out from the origin to determine the value. The X value is 2.

Then, look at where the point is located on the y-axis. Again, there is no label for values on the map, so count up from the origin. The Y value is 3.

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

Video Review

Explore More

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 Explore More Problems

To view the Explore More answers, open this PDF file and look for section 2.14. 

Vocabulary

x-axis

x-axis

The x-axis is the horizontal axis in the coordinate plane, commonly representing the value of the input or independent variable.
y axis

y axis

The y-axis is the vertical number line of the Cartesian plane.
Abscissa

Abscissa

The abscissa is the x-coordinate of the ordered pair that represents a plotted point on a Cartesian plane. For the point (3, 7), 3 is the abscissa.
Cartesian Plane

Cartesian Plane

The Cartesian plane is a grid formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin.
Coordinate grid

Coordinate grid

The coordinate grid is formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin. The coordinate grid is also called a Cartesian Plane or coordinate plane.
Coordinate Plane

Coordinate Plane

The coordinate plane is a grid formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin. The coordinate plane is also called a Cartesian Plane.
Coordinates

Coordinates

The coordinates of a point represent the point's location on the Cartesian plane. Coordinates are written in ordered pairs: (x, y).
Ordered Pair

Ordered Pair

An ordered pair, (x, y), describes the location of a point on a coordinate grid.
Ordinate

Ordinate

The ordinate is the y-coordinate of the ordered pair that represents a plotted point on a Cartesian plane. For the point (3, 7), 7 is the ordinate.
Origin

Origin

The origin is the point of intersection of the x and y axes on the Cartesian plane. The coordinates of the origin are (0, 0).

Image Attributions

  1. [1]^ License: CC BY-NC 3.0
  2. [2]^ License: CC BY-NC 3.0
  3. [3]^ License: CC BY-NC 3.0
  4. [4]^ License: CC BY-NC 3.0
  5. [5]^ License: CC BY-NC 3.0
  6. [6]^ License: CC BY-NC 3.0
  7. [7]^ License: CC BY-NC 3.0
  8. [8]^ License: CC BY-NC 3.0
  9. [9]^ License: CC BY-NC 3.0

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