Plotting Points on the Coordinate Plane
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This example demonstrates how to plot points on a coordinate plane. It involves core mathematical concepts such as coordinate system usage and point representation. Key construction elements include commands like Random, Circle, Ray, OrthogonalLine, Intersect, CircumcircleArc, Midpoint, Sequence, If, Segment, Polygon, Line, Rotate, Mod, and objects like Point. Suitable for middle school and above students for practicing and reinforcing coordinate geometry skills.
GeoGebra Commands & Parameters
Random(-10, 10) → bbRandom(-10, 10) → aaRandom(-10, 10) → ccRandom(4, 15) → rrCircle(A, (((1.5 * v) - 1) * rr)) → c'Ray(A, (0, 0)) → aOrthogonalLine(A, a) → bIntersect(c', b) → B, CIntersect(c', a) → D, TCircumcircleArc(B, D, C) → dMidpoint(C, D) → EMidpoint(B, D) → F_2Ray(A', E) → eRay(A', F_2) → fIntersect(d, e) → G,Intersect(d, f) → H,CircumcircleArc(G, D, H) → gCircle(I, 1) → hSequence(Text[If[s < 10, " ", ""] + (s), (21.6 + (2 * Mod[s - 1, 3]), 7.75 - (2 * Div[s - 1, 3]))], s, 1, 12) → liste3Circle(J, 1) → kSequence(Text[If[s ≟ 1, " ", If[s < 5, " ", ""]] + ((30 * (s - 1))) + "º", (21.25 + (2 * Mod[s - 1, 3]), -6.25 - (2 * Div[s - 1, 3]))], s, 1, 12) → liste4If(yB > -5, 5°, ((((xB - (3 * yB)) / 2 - 19 - 1) * 30))°) → angIf(ang ≟ α ∧ dist ≟ rr, true, false) → razSegment(O, N) → mCircle(A, (((2 * v) - 1) * rr) - n) → pSequence(Circle[A, (((1.5 * v) - 1) * rr) - i], i, 0, n, n / 10) → liste5Polygon(P, Q, R, S) → poly1, p_1, q, r_1, sCircle((0, 0), If[((2 * v) * rr) > 12, 0, ((2 * v) * rr)]) → cMidpoint(K, L) → UMidpoint(U, L) → VMidpoint(U, V) → WMidpoint(V, L) → ZSegment(K, C_1) → lLine(A, l) → iSegment(A, U) → tIntersect(c, t) → A_1, B_1Segment(U, A_1) → a_1Rotate(C_1, (6 * v), U) → L'Segment(U, L') → b_1Mod((v * 100), 2) → abSegment(O, D_1) → jCircle(O, C_1) → g_1Point(g_1) → E_1Segment(O, E_1) → h_1Circle(F_1, 6.5 - abs(r / 4.5)) → q_1Line(F_1, l) → i_1Intersect(q_1, i_1) → G_1, H_1Line(J_1, r_1) → j_1Point(j_1) → N_1Line(N_1, l) → l_1Line(J_1, l) → m_1Point(m_1) → O_1Point(l_1) → P_1Intersect(l_1, r_1) → M_1Polygon(M_1, N_1, J_1, F) → poly2, m_2, n_1, j_2, f_2Point(l_1) → Q_1Point(m_1) → R_1Polygon(P_1, Q_1, R_1, O_1) → poly3, p_2, q_2, r_2, o_1Point(j_1) → S_1Polygon(S_1, T_1, O_1, J_1) → poly4, s_1, t_1, o_2, j_3Midpoint(s_1) → V_1Midpoint(o_2) → W_1Midpoint(S_1, J_1) → Z_1Midpoint(t_1) → A_2Segment(V_1, W_1) → a_2Segment(Z_1, A_2) → b_2Intersect(b_2, a_2) → B_2Circle(B_2, V_1) → c_2Sequence((x(O) + i, y(D_1)), i, -11, 11, 1) → liste1Sequence((x(N) + i, y(N)), i, -11, 11, 1) → liste6Sequence((x(C_1), y(C_1) + i), i, -11, 11, 1) → liste7Sequence((x(E_1), y(E_1) + i), i, -11, 11, 1) → liste8Ray(M_1, T_1) → c_1Sequence(Segment[Element[liste8, i], Element[liste7, i]], i, 0, 22) → liste10Sequence((x(D_1) + i, 0), i, -11, 11) → liste2Sequence(Segment[Element[liste1, i], Element[liste6, i]], i, 0, 22) → liste9Line(S, P) → d_1Line(J_1, S_1) → e_1Line(Q_1, e_1) → f_1Intersect(d_1, s) → MIntersect(d_1, f_1) → C_2Line(R, d_1) → k_1Intersect(e_1, k_1) → D_2Polygon(S, C_2, Q_1, S_1, D_2, R) → poly5, s_2, c_3, q_3, s_3, d_2, r_3Point(d_1) → E_2Line(E_2, p_1) → e_2Intersect(k_1, e_2) → G_2Polygon(E_2, P, Q, G_2) → poly6, e_3, p_3, q_4, g_2Sequence(O + (i, 0), i, -10, 10) → liste11Sequence(O + (0, i), i, -10, 10) → liste12Sequence(i, i, -10, 10) → liste13Sequence(Text[Element[liste13, i], (x(Element[liste11, i] - 0.42), y(Element[liste11, i] - 0.85))], i, 1, Length[liste13], 2) → liste14Sequence(Text[Element[liste13, i], (x(Element[liste12, i] - 1), y(Element[liste12, i] - 0.31))], i, 1, Length[liste13], 2) → liste15