Cartesian Coordinates
High School
Definition
Cartesian coordinates are also called rectangular coordinates. Part of the Cartesian Coordinates System where points are on a plane signified by a pair of numerical coordinates. There are two perpendicular lines that make up the axis of the plane and they meet at the origin, usually with the coordinates of (0,0).
Worked examples
\(A = (3, 5)\)
Point A is 3 units right and 5 units up from the origin \((0,0)\).
\(B = ({-2}, 4) \quad C = (1, {-3})\)
Negative coordinates mean left (x) or down (y) from the origin.
\(\)Origin\( = (0, 0)\)
The origin is where the x-axis and y-axis meet; both coordinates are zero.
Common mistakes
- \((5, 3)\) and \((3, 5)\) are the same point → \((5, 3)\) is 5 right, 3 up; \((3, 5)\) is 3 right, 5 up Order matters: the first number is always x, the second is always y.
- \(({-4}, 2)\) is in Quadrant IV → \(({-4}, 2)\) is in Quadrant II Negative x and positive y means Quadrant II (upper left).
- Writing \((y, x)\) instead of \((x, y)\) → Always write \((x, y)\) Convention is x-coordinate first, y-coordinate second.
Where you'll use it next
Cartesian coordinates are the foundation for graphing lines and curves, transformations, distance and midpoint formulas, and later work in vectors, calculus, and analytic geometry.
Found in 1 StudyPug lesson
Mastering the Cartesian Plane: A Complete Guide
7th Grade7thGrade 7 Math
Unlock the power of the Cartesian plane with our in-depth guide. Learn to plot points, navigate quadrants, and apply concepts to real-world problems. Perfect for students at all levels.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026