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Calculating Vertical Distance Between Points A and E

Calculating Vertical Distance Between Points A and E
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2015-08-13 03:00
FunctionCoordinate GeometryGeometric ConstructionGraphing
In collections CCSS Support Algebra I Unit 3
This example demonstrates how to find the vertical distance between two points A and E in a coordinate plane. Key mathematical concepts include coordinate geometry, point coordinates, vertical distance calculation, and linear equations. The GeoGebra construction uses Polygon to create a trapezoid figure for visualization, Point commands to define coordinates of points A and E, Segment to show the vertical relationship, Slider animations to demonstrate parameter variations, and LaTeX to display the exact distance formula. Suitable for middle and high school mathematics teaching, particularly useful for introducing coordinate geometry concepts and distance formula derivations.

GeoGebra Commands & Parameters

  1. SelectedIndex(Y_2) → Y2
  2. SelectedIndex(X_2) → X2
  3. SelectedIndex(X_1) → X1
  4. Polygon(WhiteA, WhiteB, WhiteC, WhiteD) → White, Whitea, Whiteb, Whitec, Whited
  5. LaTeX("\text{Use the buttons below to return to the original problem or}") → Final1
  6. LaTeX("\text{randomly generate a similar practice problem.}") → Final2
  7. LaTeX("\text{Take the absolute value of the difference.}") → Ans1_8
  8. LaTeX("\text{Subtract the values of the \textcolor{#000099}{y}-coordinates.}") → Ans1_3
  9. LaTeX((("\text{The difference of the \textcolor{#000099}{y}-coordinates is \textcolor{#000099}{" * nine) * "}.}")) → Ans1_7
  10. LaTeX("\text{number line.}") → Ans1_{10}
  11. LaTeX("\text{The absolute value is a number’s distance from \textcolor{#000099}{0} on a }") → Ans1_9
  12. LaTeX((("\text{The vertical distance between points \textcolor{#000099}{A} and \textcolor{#000099}{E} is \textcolor{#000099}{" * nine) * "} units.}")) → Ans1_{12}
  13. LaTeX("\text{y}") → text1_1
  14. LaTeX("\text{Find the vertical distance between points \textcolor{#000099}{A} and \textcolor{#000099}{E}.}") → Question1
  15. Point(Whited) → H
  16. LaTeX((((((((("\text{Because \textcolor{#000099}{" * nine) * "} is \textcolor{#000099}{") * nine) * "} units away from \textcolor{#000099}{0}, |\textcolor{#000099}{") * nine) * "}|=\textcolor{#000099}{") * nine) * "}.}")) → Ans1_{11}
  17. LaTeX("\text{Identify the \textcolor{#000099}{y}-coordinate of both points.}") → Ans1
  18. Polygon(WhiteA_1, WhiteB_1, WhiteC_1, WhiteD_1) → White_1, Whitea_1, Whiteb_1, Whitec_1, Whited_1
  19. Segment(M, N) → a
  20. Segment(N, O) → b
  21. Segment(O, P) → c
  22. Polygon(Graph_hi, Graph_hi2, Graph_hi4, Graph_hi3) → Graph, e_1, f_1, g_1, h_1
  23. Element(X_1, SelectedIndex[X_1]) → num
  24. SelectedIndex(Y_1) → Y1
  25. LaTeX((("\text{The \textcolor{#000099}{y}-coordinate of point \textcolor{#000099}{A} is \textcolor{#000099}{" * X2) * "},and the \textcolor{#000099}{y}-coordinate of}")) → Ans1_4
  26. LaTeX((((((("\text{Point \textcolor{#000099}{A} is located at (\textcolor{#000099}{" * X1) * "}, \textcolor{#000099}{") * X2) * "}).Therefore,its \textcolor{#000099}{y}-coordinate is \textcolor{#000099}{") * X2) * "}.}")) → Ans1_1
  27. LaTeX((((((("\text{Point \textcolor{#000099}{E} is located at (\textcolor{#000099}{" * Y1) * "}, \textcolor{#000099}{–") * Y2) * "}).Therefore,its \textcolor{#000099}{y}-coordinate is \textcolor{#000099}{–") * Y2) * "}.}")) → Ans1_2
  28. LaTeX((((((("\text{\textcolor{#000099}{" * X2) * "} – (\textcolor{#000099}{–") * Y2) * "}) = \textcolor{#000099}{") * nine) * "}}")) → Ans1_6
  29. LaTeX("\text{Select coordinates for A and E:}") → text3
  30. LaTeX("\text{DATA KIT}") → text2
  31. LaTeX((("\text{point \textcolor{#000099}{E} is \textcolor{#000099}{–" * Y2) * "}. Subtract to find the difference.}")) → Ans1_5
  32. Polygon(E_2, F_2, G_2, H_2) → poly1, e_2, f_2, g_2, h_2
  33. Polygon(I_2, H_2, J_2, K_2) → poly2, i_2, h_3, j_2, k_2
  34. Polygon(O_2, T_2, U_2, V_2) → poly3, o_2, t_2, u_2, v_2
  35. Polygon(W_2, Z_2, A_3, B_3) → poly4, w_2, z_2, a_3, b_3
  36. LaTeX("\text{Quantitative variables are variables measured on a }") → text5_1
  37. LaTeX("\text{numeric scale. }") → text5_2
  38. LaTeX("\text{Quantitative variables: }") → text5