Coordinate Geometry
Lessons in this chapter
About Coordinate Geometry
Coordinate Geometry introduces the grid that algebra and geometry meet on, and it is the first time a pair of numbers names a single location.
Plot Points on a Coordinate Plane establishes the convention that everything else depends on: the first number is horizontal, the second is vertical, and the order is not negotiable. The point (3, 5) is not the point (5, 3), and swapping them is the universal beginner error.
Relate Points on a Coordinate Plane asks how points sit with respect to one another. Points sharing an x-coordinate line up vertically, points sharing a y-coordinate line up horizontally, and the distance between two points on the same line is the difference of the coordinates that change.
Plot and Interpret Line Graphs and Analyze Numeric Patterns puts the plane to work. Plotting a numeric pattern turns a rule like “add three each time” into a straight line, and seeing that a constant step produces a straight line is the idea 6th and 7th grade build linear equations on.
All three lessons open as a 5th grade math worksheet in the page. Plot Points on a Coordinate Plane, Relate Points on a Coordinate Plane and Plot and Interpret Line Graphs and Analyze Numeric Patterns each set their own questions, marked as you answer them. They are free to try, with no login needed for your first 3.
Frequently asked questions
Plot Points on a Coordinate Plane establishes the convention everything else depends on, that the first number is horizontal and the order is not negotiable. Relate Points on a Coordinate Plane asks how points sit with respect to one another, and Plot and Interpret Line Graphs and Analyze Numeric Patterns puts the plane to work, turning a rule like add three each time into a straight line. The coordinate plane sits in Geometry (5.G) and the numeric patterns in Operations and Algebraic Thinking (5.OA).
Two number lines crossing at right angles. Any point is named by a pair of numbers giving its horizontal and vertical position.
Go 3 along the horizontal axis and 5 up the vertical one. The order matters: (5, 3) is a different point entirely.
Reversing the coordinates, going up first and then across. The fixed convention is along, then up.
The point (0, 0) where the two axes cross. It is the starting point for every other coordinate.
Subtract the coordinates that differ. Points (2, 7) and (2, 3) share an x-coordinate, so the distance is 7 − 3, which is 4.