Rotated point practice
Author: Guy Barmoha

Move Point A around and see if you can put the colored points in the correct position. You will know if you are correct.

Point A is the original point.
Point B should be the rotation of Point A about the origin 90 degrees.
Point C should be the rotation of Point A about the origin 180 degrees.
Point D should be the rotation of Point A about the origin 270 degrees.
Point E should be the rotation of Point A about the origin 360 degrees.

Recta

AB

AC

AD

AE

BC

BD

BE

CD

CE

DE

Pendiente

Ord.Origen

Ecuación

PUNTUACIÓN:

A = (-4, 1)
B = (-2, 3)
C = (6, 5)
D = (4, -3)
E = (2, -5)
P = (1, 2)
Q = (3, 3)
P' = If(x(P)  <  x(Q), P, Q)
Q' = If(x(P)  <  x(Q), Q, P)
u = Vector(P, Q)
r = Line(P, Q)
k: sgn(Slope[r])
B2 = NaN
B3 = NaN
B4 = NaN
B5 = NaN
B6 = NaN
B7 = NaN
B8 = NaN
B9 = NaN
B10 = NaN
B11 = NaN
C2 = NaN
C3 = NaN
C4 = NaN
C5 = NaN
C6 = NaN
C7 = NaN
C8 = NaN
C9 = NaN
C10 = NaN
C11 = NaN
sB2: y(B - A) / x(B - A)
sB3: y(C - A) / x(C - A)
sB4: y(D - A) / x(D - A)
sB5: y(E - A) / x(E - A)
sB6: y(C - B) / x(C - B)
sB7: y(D - B) / x(D - B)
sB8: y(E - B) / x(E - B)
sB9: y(D - C) / x(D - C)
sB10: y(E - C) / x(E - C)
sB11: y(E - D) / x(E - D)
sC2: y(A) - (x(A) * sB2)
sC3: y(A) - (x(A) * sB3)
sC4: y(A) - (x(A) * sB4)
sC5: y(A) - (x(A) * sB5)
sC6: y(B) - (x(B) * sB6)
sC7: y(B) - (x(B) * sB7)
sC8: y(B) - (x(B) * sB8)
sC9: y(C) - (x(C) * sB9)
sC10: y(C) - (x(C) * sB10)
sC11: y(D) - (x(D) * sB11)
test2 = If(B2 ≟ sB2 ∧ C2 ≟ sC2, 1, 0)
test3 = If(B3 ≟ sB3 ∧ C3 ≟ sC3, 1, 0)
test4 = If(B4 ≟ sB4 ∧ C4 ≟ sC4, 1, 0)
test5 = If(B5 ≟ sB5 ∧ C5 ≟ sC5, 1, 0)
test6 = If(B6 ≟ sB6 ∧ C6 ≟ sC6, 1, 0)
test7 = If(B7 ≟ sB7 ∧ C7 ≟ sC7, 1, 0)
test8 = If(B8 ≟ sB8 ∧ C8 ≟ sC8, 1, 0)
test9 = If(B9 ≟ sB9 ∧ C9 ≟ sC9, 1, 0)
test10 = If(B10 ≟ sB10 ∧ C10 ≟ sC10, 1, 0)
test11 = If(B11 ≟ sB11 ∧ C11 ≟ sC11, 1, 0)
r2 = Line((0, C2), (1, B2 + C2))
r3 = Line((0, C3), (1, B3 + C3))
r4 = Line((0, C4), (1, B4 + C4))
r5 = Line((0, C5), (1, B5 + C5))
r6 = Line((0, C6), (1, B6 + C6))
r7 = Line((0, C7), (1, B7 + C7))
r8 = Line((0, C8), (1, B8 + C8))
r9 = Line((0, C9), (1, B9 + C9))
r10 = Line((0, C10), (1, B10 + C10))
r11 = Line((0, C11), (1, B11 + C11))
D2 = LaTeX(r2)
D3 = LaTeX(r3)
D4 = LaTeX(r4)
D5 = LaTeX(r5)
D6 = LaTeX(r6)
D7 = LaTeX(r7)
D8 = LaTeX(r8)
D9 = LaTeX(r9)
D10 = LaTeX(r10)
D11 = LaTeX(r11)
E2 = If(test2 ≟ 1, "BIEN", "?")
E3 = If(test3 ≟ 1, "BIEN", "?")
E4 = If(test4 ≟ 1, "BIEN", "?")
E5 = If(test5 ≟ 1, "BIEN", "?")
E6 = If(test6 ≟ 1, "BIEN", "?")
E7 = If(test7 ≟ 1, "BIEN", "?")
E8 = If(test8 ≟ 1, "BIEN", "?")
E9 = If(test9 ≟ 1, "BIEN", "?")
E10 = If(test10 ≟ 1, "BIEN", "?")
E11 = If(test11 ≟ 1, "BIEN", "?")
E13 = Text("" + (test2 + test3 + test4 + test5 + test6 + test7 + test8 + test9 + test10 + test11))
F = If(y(Q)  <  y(P), (x(P), y(Q)), (x(Q), y(P)))
F' = If(y(Q) ≟ y(F), (x(Q), y(Q + u)), F)
G: ((x(P') + x(Q')) / 2, Min[y(P'), y(Q')])
I = Intersect(r, yAxis)
texto1: "" + (round(x(Q' - P')))
texto2: "" + (round(y(Q' - P')))
texto3: "" + (FractionText[y(I)])
H: (If[y(Q') > y(P'), x(Q') + 0.1, x(P') + 0.1], (y(P') + y(Q')) / 2 + 0.2)
lista3 = Sequence(Polygon[F' + (t * u), Q + (t * u), Q + (t * u) + (k * ((x(Q' - P') * (15 - ((k * sgn(x(Q - P))) * t))), 0)), F' + (t * u) + (k * ((x(Q' - P') * (15 - ((k * sgn(x(Q - P))) * t))), 0))], t, -15, 15)
lista1 = Sequence(Segment[P + (s * u), F + (s * u)], s, -15, 15)
lista2 = Sequence(Segment[F + (s * u), Q + (s * u)], s, -15, 15)