Humanitas4All Learning - Euclidean/Coordinate Plane, Ordered Pairs

Euclidean/Coordinate Plane, Ordered Pairs

What is a coordinate plane?

A coordinate plane is a system that uses one or numbers (coordinates) to determine a position of a point on something such as a Euclidean plane (shown left).

The left-right (horizontal) direction is known as x (referred to as the x-axis).

- As x increases, the point moves right

- As x decreases, the point moves left

The up-down (vertical) direction is known as y (referred to as the y-axis).

- As y increases, the point moves up

- As y decreases, the point moves down

Writing Ordered Pairs

Follow the format of an ordered pair: (x, y)

x: Find the horizontal distance along the x-axis (how far left or right?)
y: Find the vertical distance along the y-axis (how far up or down?)

If x is positive, the point goes to the right

If y is positive, the point goes up

Example 1: What does the point (0, 9) indicate?

→ 0 units to the right and 9 units up

→ In other words, this point is simply 9 units up on the y-axis because the point moved 0 units on the x-axis

Example 2: What does the point (3, 2) indicate?

→ 3 units to the right, 2 units up

Example 3: What does the point (1,8) indicate?

→ 1 unit right (x-axis), 8 units up (y-axis)

Example 4: Plot (12, 5) on a plane

→ this ordered pair indicates a point 12 units to the right, 5 units up

Example 5: Plot (0,5) on the coordinate plane

→ this ordered pair indicates a point 6 units to the right (on the x-axis) and 4 units up (on the y-axis)

Ordered pairs are also referred to as Cartesian coordinates or Rectangular coordinates

They are called Cartesian because the idea was developed by mathematician Rene Descartes, who was also known as Cartesius
They are called Rectangular because the point creates a rectangle with the x-axis and the y-axis

Negative numbers are numbers less than zero

If x is negative, the point goes to the left

If y is negative, the point goes down

Example 1: Plot (-3,2)

→ this ordered pair indicates a point 3 units to the left (on the x-axis) and 2 units up (on the y-axis)

Example 2: Plot (-2, -4)

→ this ordered pair indicates a point 2 units to the left (on the x-axis) and 4 units down (on the y-axis)

Example 3: Plot (3, -3)

→ this ordered pair indicates a point 3 units to the right (on the x-axis) and 3 units down (on the y-axis)

What are the 4 quadrants?

The 4 quadrants of the coordinate plane are numbered in a counterclockwise direction, starting from the top right corner.

Notice “the origin,” or middle of the plane is (0,0). The point (0, 0) is referenced with the letter “O” because it is located at the center of the plane.

Quadrant 1 (I) is the top right quadrant (x, y)

Quadrant 2 (II) is the top left quadrant (-x,y)

Quadrant 3 (III) is the bottom left quadrant (-x,-y)

Quadrant 4 (IV) is the bottom right quadrant (x,-y)