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The Coordinate Plane (Cartesian Plane)

The Coordinate Plane (Cartesian Plane)
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2026-03-08 18:56
Coordinate GeometryGeometric ConstructionGraphing
In collections Coordinate Geometry
The coordinate plane is a fundamental concept in mathematics used to describe points and graphs in two-dimensional space. This example explores the main definitions of the coordinate plane, complemented by scaffolding activities and assessment of knowledge and skills. Through this example, students can gain a deeper understanding of the basic concepts of the coordinate plane, including coordinate axes, coordinate points, and the distance formula. The example uses GeoGebra to construct an interactive graph that allows students to explore various aspects of the coordinate plane. Suitable for middle school and high school mathematics courses, particularly geometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. Shuffle({1, 2, 3}) → allCaseNum, {1, 3, 2}
  2. Element(allCaseNum, Mod[countQuestion, Length[allCaseNum]] + 1) → caseNum
  3. Polygon({GRMIN + ((-offX), (-offY)), (x(GRMAX), y(GRMIN)) + (offX, (-offY)), GRMAX + (offX, offY), (x(GRMIN), y(GRMAX)) + ((-offX), offY)}) → peep
  4. SelectedIndex(ddMenu) → is
  5. Sequence((k, 0), k, -10, 10, 1) → xGrid
  6. Sequence((0, k), k, 1, 16, 1) → yGrid
  7. PointIn(peep) → ONBPT
  8. circlePixels(ONBPT, 7 + (7 * pulsing), (xMin, yMin), (xMax, yMax), (PXwidth, PXheight)) → pulsingObject
  9. Segment((x(GRMIN) - offX, 0), (x(GRMAX) + offX, 0)) → fakeX
  10. Segment((0, y(GRMIN) - offY), (0, y(GRMAX) + offY)) → fakeY
  11. Join(Sequence[Sequence[(j, k), j, x(GRMIN), x(GRMAX), 1], k, y(GRMIN), y(GRMAX), 1]) → bigGrid
  12. Polygon({O, (x(GRMAX) + offX, 0), GRMAX + (offX, offY), (0, y(GRMAX) + offY)}) → quad1
  13. Mirror(quad1, x = 0) → quad2
  14. Mirror(quad2, y = 0) → quad3
  15. Mirror(quad3, x = 0) → quad4
  16. Segment((x(GRMIN) - offX, 0), (x(GRMAX) + offX, 0)) → fakeX2
  17. Segment((0, y(GRMIN) - offY), (0, y(GRMAX) + offY)) → fakeY2
  18. Point(bigGrid) → P
  19. Segment(P, PX) → projX
  20. Segment(P, PY) → projY
  21. Segment(O, PX) → asc
  22. Segment(O, PY) → ord
  23. If(x(P) > 0 ∧ y(P) > 0, "in quadrant I", x(P) ≟ 0 ∧ y(P) ≠ 0, "on the \(y-\)axis", "on the \(x-\)axis", x(P) > 0 ∧ y(P) < 0, "in quadrant IV", x(P) < 0 ∧ y(P) > 0, "in quadrant II", x(P) < 0 ∧ y(P) < 0, "in quadrant III", x(P) ≟ 0 ∧ y(P) ≟ 0, "at the origin") → textQuadrNum
  24. If(x(P) > 0, "positive", x(P) < 0, "negative", "zero") → textSegnX
  25. If(y(P) > 0, "positive", y(P) < 0, "negative", "zero") → textSegnY
  26. If(x(P) > 0, ">0", x(P) < 0, "<0", "=0") → textVersX
  27. If(y(P) > 0, ">0", y(P) < 0, "<0", "=0") → textVersY

AI Drawing Prompt Reference

Draw a Cartesian coordinate plane with a grid, axes extending from -10 to 10, and the origin marked. Shade the four quadrants with semi-transparent colors: first quadrant upper right, second upper left, third lower left, fourth lower right. Place a random point on the grid, draw perpendicular dashed segments from it to both axes, and mark the foot points. Display the signs of its x and y coordinates (positive, negative, or zero) and a text label indicating which quadrant or axis it lies on. Extend the axes slightly beyond the grid.
The prompt above was compiled from the original drawing commands and is for reference only.