Math  /  Geometry

QuestionTransformaciones y figuras geometricas Escribir una regla para describir una rotación
I triángulo RSTR S T se rota 270270^{\circ} en sentido antihorario en torno al origen. 1 resultado es RST\triangle R^{\prime} S^{\prime} T^{\prime} tal como se muestra a continuación. (a) Las flechas a continuación muestran que las coordenadas de la izquierda se asignan a las coordenadas de la derecha. Llenar los espacios vacios para dar las coordenadas tras haber realizado la rotación. coordenadas originales \rightarrow coordenadas finales R(8,1)R(,Π)S(6,7)S(,)T(2,3)T(,)\begin{array}{r} R(-8,1) \rightarrow R^{\prime}(\square, \Pi) \\ S(-6,7) \rightarrow S^{\prime}(\square, \square) \\ T(-2,-3) \rightarrow T^{\prime}(\square, \square) \end{array} (b) Elegir la regla general que describe la rotación de RST\triangle R S T a RST\triangle R^{\prime} S^{\prime} T^{\prime}. (x,y)(x,y)(x, y) \rightarrow(-x,-y) (x,y)(x,y)(x, y) \rightarrow(-x, y) (x,y)(y,x)(x, y) \rightarrow(y,-x) (x,y)(y,x)(x, y) \rightarrow(y, x) (x,y)(x,y)(x, y) \rightarrow(x,-y) (x,y)(y,x)(x, y) \rightarrow(-y, x) (x,y)(y,x)(x, y) \rightarrow(-y,-x)

Studdy Solution

STEP 1

1. The rotation is about the origin.
2. The rotation is 270270^\circ counterclockwise.

STEP 2

1. Understand the effect of a 270270^\circ counterclockwise rotation on coordinates.
2. Apply the rotation rule to each vertex of the triangle.
3. Determine the general rule for the rotation.

STEP 3

Understand the effect of a 270270^\circ counterclockwise rotation on coordinates. A 270270^\circ counterclockwise rotation is equivalent to a 9090^\circ clockwise rotation. The rule for this transformation is:
(x,y)(y,x) (x, y) \rightarrow (y, -x)

STEP 4

Apply the rotation rule to each vertex of the triangle:
For R(8,1) R(-8, 1) : R=(1,8) R' = (1, 8)
For S(6,7) S(-6, 7) : S=(7,6) S' = (7, 6)
For T(2,3) T(-2, -3) : T=(3,2) T' = (-3, 2)

STEP 5

Determine the general rule for the rotation. Based on the transformation applied to each point, the general rule is:
(x,y)(y,x) (x, y) \rightarrow (y, -x)
The coordinates after rotation are: - R(8,1)R(1,8) R(-8, 1) \rightarrow R'(1, 8) - S(6,7)S(7,6) S(-6, 7) \rightarrow S'(7, 6) - T(2,3)T(3,2) T(-2, -3) \rightarrow T'(-3, 2)
The general rule for the rotation is: (x,y)(y,x) (x, y) \rightarrow (y, -x)

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