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Calculate Profit or Loss Percentage

Calculate Profit or Loss Percentage
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2020-11-14 14:37
Geometric Construction
This example demonstrates how to use GeoGebra to calculate and visualize profit or loss percentage. The core math concepts involved include algebra, arithmetic, and percentage calculations. Construction highlights involve using commands like If for conditional logic, Point and Polygon objects to create shapes, Sequence to generate sequence data, Textfield and Segment to display and construct graphical elements, and Vector to represent vectors. Suitable for middle school students and above to learn and understand basic concepts in business mathematics.

GeoGebra Commands & Parameters

  1. If(a, "d", ((If[p ∧ x(P) < 10, "-"] * abs(d)) * "")) → dtext
  2. If(c', "c", (n * "")) → ntext
  3. Point(yAxis) → A
  4. Point(yAxis) → B
  5. If(x(P) ≤ 10, A + (10, 0), B + (10, 0)) → A0
  6. If(x(P) ≤ 10, P, (x(P), y(B))) → P0
  7. Polygon(P, Q, (0, y(Q)), (0, y(P))) → q1, p_1, q_1, g, h
  8. Polygon({P0, A0, A0 + (0, 1), P0 + (0, 1)}) → q2
  9. Polygon({B, B + (10, 0), B + (10, 1), B + (0, 1)}) → q3
  10. Polygon({B, B + (10, 0), B + (10, 1), B + (0, 1)}) → q4
  11. Sequence(Segment[B + (i, 0), B + (i, 1)], i, 1, 9, 1) → l1
  12. Sequence(Sequence[Segment[B + (j + i, 0), B + (j + i, 1)], j, 0, 9, 1], i, 0.1, 0.9, 0.1) → l2
  13. Sequence(Segment[A + (i, 0), A + (i, 1)], i, 1, 9, 1) → l3
  14. Sequence(Sequence[Segment[A + (j + i, 0), A + (j + i, 1)], j, 0, 9, 1], i, 0.1, 0.9, 0.1) → l4
  15. Textfield(n) → InputBox1
  16. Textfield(m) → InputBox2
  17. If(b, "s", (m * "")) → mtext
  18. Segment(If[b_1 ≟ 0, A, A0] + (0, 1.2), If[b_1 ≟ 0, A, A0] + (0, 1.5)) → i
  19. Segment(If[b_1 ≟ 0, P, P0] + (0, 1.2), If[b_1 ≟ 0, P, P0] + (0, 1.5)) → j
  20. Vector(Midpoint[i], Midpoint[j]) → u
  21. Vector(Midpoint[j], Midpoint[i]) → v
  22. Segment(A0 - (0, 0.2), A0 - (0, 0.5)) → k
  23. Segment(P0 - (0, 0.2), P0 - (0, 0.5)) → l
  24. Vector(Midpoint[k], Midpoint[l]) → w
  25. Vector(Midpoint[l], Midpoint[k]) → e
  26. Segment(B + (0, 1.2), B + (0, 1.5)) → f
  27. Segment(B + (10, 1.2), B + (10, 1.5)) → r
  28. Vector(Midpoint[f], Midpoint[r]) → s
  29. Vector(Midpoint[r], Midpoint[f]) → t
  30. Segment(B - (0, 0.2), B - (0, 0.5)) → f_1
  31. Segment(B + (10, -0.2), B + (10, -0.5)) → g_1
  32. Vector(Midpoint[f_1], Midpoint[g_1]) → u_1
  33. Vector(Midpoint[g_1], Midpoint[f_1]) → v_1
  34. If(a, "d", If[b, If[b_1 ≟ 0, "s", "x"], "c"]) → text12
  35. Sequence(Segment[A + (10 + i, 0), A + (10 + i, 1)], i, 0.1, x(P) - 10, 0.1) → l6
  36. Sequence(Segment[A + (10 + i, 0), A + (10 + i, 1)], i, 0, floor(x(P) - 10)) → l5
  37. Sequence(Segment[A0 + (i, 0), A0 + (i, 1)], i, 0, floor(x(P0) - 10)) → l7
  38. Sequence(Segment[A0 + (i, 0), A0 + (i, 1)], i, 0.1, x(P0) - 10, 0.1) → l8
  39. If(p, m - n, abs(n - m)) → c
  40. Segment(If[x(P) ≤ 10, A + (10, 0), P], If[x(P) ≤ 10, B + (10, 1), x(P)]) → h_1
  41. Segment(A, B + (0, 1)) → i_1
  42. Segment(A - (0, 0.2), A - (0, 0.5)) → j_1
  43. Segment(P - (0, 0.2), P - (0, 0.5)) → k_1
  44. Vector(Midpoint[k_1], Midpoint[j_1]) → w_1
  45. Vector(Midpoint[j_1], Midpoint[k_1]) → c_1
  46. Segment(A0 + (0, 1.2), A0 + (0, 1.5)) → k'
  47. Segment(P0 + (0, 1.2), P0 + (0, 1.5)) → l'
  48. Vector(Midpoint[k'], Midpoint[l']) → e_1
  49. Vector(Midpoint[l'], Midpoint[k']) → l_1
  50. If(p, "Change", If[x(P) < 10, "Loss", If[x(P) > 10, "Profit", ""]]) → change

AI Drawing Prompt Reference

Use a coordinate plane with a vertical axis as reference. Choose two points on the vertical axis to define the upper and lower boundaries, then construct segmented rectangle-like regions to the right: for positions at and beyond a threshold, let the left boundary be set by the vertical axis while the top and bottom edges follow the respective heights, forming polygons that emphasize a profit/loss style comparison. On the right side of the upper and lower regions, add narrow vertical band sections and subdivide them with evenly spaced short vertical segments within a specified height range, repeating the band shape to strengthen the contrast. Include small offset vertical and horizontal marker segments and draw arrow-like direction indications by connecting vectors between midpoints of selected markers. Place two numeric input text boxes and corresponding equation-style text on the figure for the displayed calculation.
The prompt above was compiled from the original drawing commands and is for reference only.