六至八年级Geometry & Topology计划中
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
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前置知识
5 项必需的前置知识（一直追溯到底）
你将学会
- 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.
定义
- 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.
定理
- 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.
常见误解
- Swapping the coordinates, plotting (3, 2) at (2, 3).
- Counting grid lines rather than unit intervals when finding distances.
通向
可选发现
- Linear algebra Points of the plane can be added and scaled as vectors, giving the vector space ℝ².