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G12 Coordinates

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G12.1 Coordinates

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Descartes

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Coordinates

We can describe the position of any point on a 2-dimensional plane using coordinates.

The coordinate of a point tells us where the point is relative to a starting point or origin.

When we write a coordinate, such as

the first number is called the x-coordinate and the second number is called the y-coordinate.

(3, 5)

x-coordinate

(3, 5)

y-coordinate

(3, 5)

the first number is called the x-coordinate and the second number is called the y-coordinate.

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4 y-axis

Using a coordinate grid

Coordinates are plotted on a grid of squares.

The x-axis and the y-axis intersect at the origin.

The coordinates of the origin are (0, 0).

The lines of the grid are numbered using positive and negative integers as follows.

O 1 2 3 4–4 –3 –2 –1

1

2

3

–4

–3

–2

–1

x-axis

origin

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third quadrant

–4

first quadrant

second quadrant

fourth quadrant

O 1 2 3 4–4 –3 –2 –1

1

2

3

4

–3

–2

–1

Quadrants

The coordinate axes divide the grid into four quadrants.

y

x

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Which quadrant?

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Coordinates

The first number in the coordinate pair tells you how many units along from the origin the point is in the x-direction.

A positive number means the point is right of the origin and a negative number means it is left.

The second number in the coordinate pair tells you how many units above or below the origin the point is in the y-direction.

A positive number means the point is above the origin and a negative number means it is below.

Remember:

Along the corridor and up (or down) the stairs.

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x

Plotting points

Plot the point (–3, 5).

0 1 2 3 4 5 6 7–1–2–3–4–5–6–7

1

2

3

4

5

6

7

–2

–4

–6

–3

–5

–7

–1

(–3, 5)

y

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x0 1 2 3 4 5 6 7–1–2–3–4–5–6–7

1

2

3

4

5

6

7

–2

–4

–6

–3

–5

–7

–1

y

Making quadrilaterals

Where could we add a fourth point to make a parallelogram?

(3, –3)

(–5, –1)

(–5, 4)

(3, 2)

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–7

Making quadrilaterals

Where could we add a fourth point to make a square?

0 1 2 3 4 5 6 7–1–2–3–4–5–6

1

2

3

4

5

6

7

–2

–4

–6

–3

–5

–7

–1x

y

(6, 2)

(2, 6)

(2, –2)

(–2, 2)

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Don’t connect three!