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The Cartesian Coordinate System
A system that specifies each point uniquely in a plane by a set of numerical coordinates.
📍Axes and Coordinates
The Axes
- • X-Axis: The horizontal number line.
- • Y-Axis: The vertical number line.
- • Origin (0,0): The point where the axes intersect.
Coordinates (x, y)
Every point is defined by an ordered pair:
- • x-coordinate (Abscissa): Distance from the y-axis.
- • y-coordinate (Ordinate): Distance from the x-axis.
◰The Four Quadrants
Quadrant I
(+, +)
Top Right
x > 0, y > 0
Quadrant II
(-, +)
Top Left
x < 0, y > 0
Quadrant III
(-, -)
Bottom Left
x < 0, y < 0
Quadrant IV
(+, -)
Bottom Right
x > 0, y < 0
📐Essential Formulas
Distance Formula
Calculates the length of the line segment connecting two points.
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Midpoint Formula
Finds the center point exactly halfway between two points.
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
🌍 Real-World Applications
- • GPS & Navigation: Latitude and Longitude are essentially coordinates on a sphere.
- • Computer Graphics: Every pixel on your screen is a coordinate (x, y).
- • Data Science: Scatter plots visualize relationships between two variables.
- • Robotics: Defining position and movement paths in space.
💡 Did You Know?
The system is named after René Descartes, a French mathematician and philosopher. Legend has it he came up with the idea while watching a fly crawl on his ceiling and realizing he could describe its position by its distance from the walls.
"I think, therefore I am." - René Descartes