3.01 Graph in the first quadrant

The coordinate plane is a two-dimensional plane used to plot points and graph lines. These points are labeled by an ordered pair of numbers of the form (x,y), called coordinates.

We can think of the coordinate plane as being built from two separate number lines. The first number line we lay down horizontally on the plane. This line is called the x-axis, and for every point in the plane we can talk about its x-coordinate, which is its horizontal position along this axis.

The second number line is placed in a vertical direction, perpendicular to the first number line. This vertical line is called the y-axis, and every point in the plane has a y,-coordinate, which is its vertical distance along this axis.

The point at which the x-axis and the y-axis intercept is called the origin. The coordinates of the origin are (0,0).

The coordinates of a point are given with respect to the origin. In the image above, we can see that the cat is 6 units to the right of the origin, and 2 units above the origin. So we can say the cat has the coordinates (6,2). The x-coordinate is 6 and the y-coordinate is 2.

Notice that the order of the numbers is important. It would be incorrect to say the cat has the coordinates (2,6). These coordinates refer to the point 2 units to the right of the origin, and 6 units above the origin.

Coordinates are always written with parentheses in the form (x,y) where the first number, x, is the x-coordinate and the second number, y is the y-coordinate.

Examples

Example 1

Consider the coordinate plane shown:

a

What object has coordinates (1, 4)?

Worked Solution

Create a strategy

Use the numbers on the axes in locating the coordinates.

Apply the idea

Start at (0, 0). Move 1 space to the right, then 4 spaces up.

The object with coordinates (1, 4) is a star.

b

What object has coordinates (10, 1)?

Worked Solution

Create a strategy

Use the numbers on the axes in locating the coordinates.

Apply the idea

Start at (0, 0). Move 10 space to the right, then 1 space up.

The object with coordinates (10, 1) is beach ball.

Example 2

Plot the point (6, 3) onto the coordinate plane.

Worked Solution

Create a strategy

Use the numbers on the axes to move on the coordinate plane.

Apply the idea

Start at (0, 0). Plot the point 6 space to the right, then 3 spaces up.

This will be the point on the plane described by (6, 3).

1

2

3

4

5

6

7

8

9

x

1

2

3

4

5

6

7

8

9

y

Watch question walkthrough

Example 3

The point with coordinates (9, 4) is:

A

9 units away from the origin vertically

B

9 units away from the origin horizontally

Worked Solution

Create a strategy

Recall that the first value (x-coordinate) represents the distance from the origin horizontally.

Apply the idea

This means the point with coordinates (9, 4) is 9 units away from the origin horizontally.

So the answer is Option B.