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Effect of Changing Coordinate Systems on a Point

Effect of Changing Coordinate Systems on a Point
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2014-02-23 20:52
Coordinate GeometryTransformationGeometric Construction
This example demonstrates how changing the origin of a coordinate system affects the coordinates of a single point. It involves core concepts like coordinate system transformation and point coordinate representation. Constructed using GeoGebra commands and objects such as TableText, Corner, Distance, Text, Line, Sequence. Suitable for high school students exploring the geometric meaning of coordinate system transformations.

GeoGebra Commands & Parameters

  1. TableText({{"0"}, {"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hc") → Xt0
  2. Corner(1) → corner1
  3. Corner(2) → corner2
  4. Corner(3) → corner3
  5. Corner(4) → corner4
  6. Corner(5) → screenDim
  7. Distance(corner1, corner2) → distX
  8. Distance(corner1, corner4) → distY
  9. Text("$(x_1,y_1)=(" + (x(O)) + "," + (y(O)) + ")$", (x(O), y(O) - 12 / unitY), true, true) → text3
  10. Line(O, xAxis) → XaxisLine
  11. Sequence(Segment[(n + x(O), y(O)), (n + x(O), y(O) - 2 / unitY)], n, (round((x(Corner[1]) - x(O)) / AxisStepX[]) * AxisStepX[]), x(Corner[2]) - x(O), AxisStepX[]) → XaxisTicks
  12. Line(O, yAxis) → YaxisLine
  13. Sequence(Segment[(x(O), y(O) + n), (x(O) - 2 / unitX, y(O) + n)], n, (round((y(Corner[1]) - y(O)) / AxisStepY[]) * AxisStepY[]), y(Corner[4]) - y(O), AxisStepY[]) → YaxisTicks
  14. Text("(x,y) = (" + (x(A)) + "," + (y(A)) + ") in black coordinate system") → text2
  15. Text("(X,Y) = (" + (x(A) - x(O)) + "," + (y(A) - y(O)) + ") in blue coordinate system") → text1
  16. Sequence(If[n ≟ 0, "", Text[TableText[{{"" + (n) + ""}, {"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hc"], (n + x(O) - (Distance[Corner[Xt0, 1], Corner[Xt0, 2]] * 0.5) - 4 / unitX, y(O) - 2 / unitY), true, true]], n, (round((x(Corner[1]) - x(O)) / AxisStepX[]) * AxisStepX[]), x(Corner[2]) - x(O), AxisStepX[]) → XaxisNumbers
  17. Sequence(If[n ≟ 0, "", Text[TableText[{{"\phantom{(}" + (n) + ""}, {"\phantom{(} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hr"], (x(O) - Distance[Corner[Xt0, 1], Corner[Xt0, 2]] - 4 / unitX, n + y(O) + (Distance[Corner[Xt0, 1], Corner[Xt0, 4]] * 0.25) + 1 / unitY), true, true]], n, (round((y(Corner[1]) - y(O)) / AxisStepY[]) * AxisStepY[]), y(Corner[4]) - y(O), AxisStepY[]) → YaxisNumbers