The coordinate plane

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عدد المتطلبات السابقة الإلزامية (حتى الأساس): 5

ستتعلّم

• 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.

تعريف

• 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.

مبرهنة

• 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.

مفاهيم خاطئة شائعة

• Swapping the coordinates, plotting (3, 2) at (2, 3).
• Counting grid lines rather than unit intervals when finding distances.

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اكتشافات اختيارية

• Linear algebra Points of the plane can be added and scaled as vectors, giving the vector space ℝ².