Grades 6–8Geometry & TopologyPlanned
The coordinate plane
Locating points with ordered pairs in all four quadrants, distances along grid lines, reflections in the axes, and plotting data and relationships.
math.geom.coordinate-plane
The lesson for this topic has not been written yet. The outline below is part of the curriculum map and has not been reviewed.
Builds on
Required prerequisites, all the way down: 5
You will learn to
- Plot and read points (x, y) with integer and rational coordinates in all four quadrants.
- Find horizontal and vertical distances between points using absolute value.
- Reflect points in the axes and describe the effect on their coordinates.
Definition
- The coordinate plane is formed by two perpendicular number lines, the x-axis and the y-axis, meeting at the origin (0, 0).
- The coordinates (a, b) of a point give its horizontal and vertical positions relative to the origin.
Theorem
- Reflecting (a, b) in the x-axis gives (a, −b), and in the y-axis gives (−a, b).
- The distance between (a, b) and (c, b) is |a − c|.
- Each point of the plane corresponds to exactly one ordered pair of real numbers.
Common misconceptions
- Swapping the coordinates, plotting (3, 2) at (2, 3).
- Counting grid lines rather than unit intervals when finding distances.
Leads to
Optional discoveries
- Linear algebra Points of the plane can be added and scaled as vectors, giving the vector space ℝ².