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Coordinate Plane

What is a Coordinate Plane?

A coordinate plane is a two-dimensional surface formed by two number lines that intersect at right angles. The horizontal number line is called the x-axis, and the vertical number line is called the y-axis.

y
x
Origin (0,0)
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
-3
-2
-1
1
2
3
-3
-2
-1
1
2
3

Origin: The point (0, 0) where the axes intersect

x-axis: The horizontal number line

y-axis: The vertical number line

Ordered Pairs

Points on the coordinate plane are represented by ordered pairs (x, y), where x is the horizontal distance from the origin and y is the vertical distance from the origin.

Plotting Points

-3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
3
(2, 3)
(-1, 1)
(-2, -2)
(3, -1)

Distance and Midpoint

Distance Formula

The distance between two points (x₁, y₁) and (x₂, y₂) can be calculated using the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]
This is an application of the Pythagorean theorem.

Example: Finding Distance

Find the distance between the points (1, 2) and (4, 6).

d = √[(4 - 1)² + (6 - 2)²]
d = √[3² + 4²]
d = √[9 + 16]
d = √25
d = 5

Midpoint Formula

The midpoint between two points (x₁, y₁) and (x₂, y₂) can be calculated using the midpoint formula:

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
The midpoint is the average of the x-coordinates and the average of the y-coordinates.

Example: Finding Midpoint

Find the midpoint between the points (1, 2) and (4, 6).

Midpoint = ((1 + 4)/2, (2 + 6)/2)
Midpoint = (5/2, 8/2)
Midpoint = (2.5, 4)

Related Topics

Practice Coordinate Plane

Test your knowledge with our interactive coordinate plane practice exercises.

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