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    es una sucesión continua de puntos infinitos que se prolongan en una misma dirección; solo posee longitud.

    Santiago

    Chicos, ¿alguien sabe la respuesta?

    obtenga es una sucesión continua de puntos infinitos que se prolongan en una misma dirección; solo posee longitud. de este sitio.

    Matemáticas Puntos y Rectas Desarrollo

    Apuntes de Matemáticas Puntos y Rectas, desarrollo

    ¿Qué es un punto?

    El punto es el elemento base de la geometría, ente fundamental, porque con él determinamos las rectas y los planos. Podemos definirlo también, como la intercesión de dos líneas. Sirve para indicar una posición y no tiene dimensión.

    ¿Qué es una recta?

    Una recta es una sucesión ininterrumpida de puntos con una misma dirección, por lo tanto sólo tiene una dimensión. Dos puntos determinan una recta la recta es infinita, no posee ni principio ni fin.

    La recta tienen una dimensión, .

    Tipos de rectasRecta: La recta propiamente dicha se caracteriza porque los puntos que la forman están en la misma dirección. Tiene una sola dirección y dos sentidos. No se puede medir.

    Semirrecta: Es línea recta que tiene origen pero no tiene fin, tiene sólo un sentido, y no se puede medir.

    Segmento: Un segmento es una línea recta que tiene principio y fin, un segmento se puede medir.

    Poligonal: Se llama recta poligonal aquella que está formada por varias porciones de rectas que están unas a continuación de otras, pero no están alineadas, la línea poligonal puede ser abierta (cuando ningún extremo se une) o cerrada (cuando el primer extremo se une con el último). La línea poligonal cerrada forma una figura plana que se llama polígono.

    Curva:Una curva está formada por puntos que están en distinta dirección. Puede ser curva abierta (los externos no se unen) curva cerrada (cuyos extremos se unen) y curva mixta (formada por lineas rectas y curvas unidas)

    Posiciones de las rectas:

    Dos rectas son paralelas: si no tienen ningún punto en común.

    Dos rectas son secantes: cuando tienen un punto en común.

    Dos rectas son perpendiculares: cuando al cortarse forman cuatro ángulos rectos.

    Posición de las rectas en el espacio

    Horizontal Vertical Inclinada

    La linea curva puede ser:

    Circunferencia, es una curva regular cerrada, cuyos puntos están todos a la misma distancia de otro llamado centro.

    Elípse, es una curva regular cerrada que se diferencia de la anterior porque la suma de la distancia de cada uno de sus puntos respecto a otros dos que están en su interior es siempre igual.

    Espiral es una curva regular abierta que gira sobre sí misma.

    Parábola es una curva regular abierta, cada uno de sus puntos está a una distancia siempre igual de un punto fijo llamado foco y de una recta llamada directriz.

    Problemas de ángulos

    Geometría Conceptos Generales

    Más apuntes de matemáticas

    fuente : www.estudiantes.info

    Recta

    Recta

    Ir a la navegación Ir a la búsqueda

    Para otros usos de este término, véase Recta (desambiguación).

    Las líneas roja y azul de este gráfico tienen la misma pendiente; las líneas roja y verde tienen la misma intersección con el eje (cruzan el eje en el mismo lugar).

    Representación de un segmento de recta.

    En geometría euclidiana, la recta o la línea recta es una línea que se extiende en una misma dirección; por lo tanto, tiene una sola dimensión y contiene un número infinito de puntos. Dicha recta también se puede describir como una sucesión continua de puntos extendidos en una sola dirección.

    Es uno de los entes geométricos fundamentales, junto al punto y el plano. Son considerados conceptos apriorísticos, ya que su definición solo es posible a partir de la descripción de las características de otros elementos similares. Un ejemplo de las dificultades de la definición de la recta a partir de puntos es la llamada paradoja de Zenón de la dicotomía, que ilustraba la desaparición de la recta al dividirla en puntos porque luego no había un concepto para ensamblar dicha recta a partir de puntos, ya que la unión de dos puntos es un punto. Las rectas se suelen denominar con una letra minúscula.

    En geometría analítica las líneas rectas en un plano pueden ser expresadas mediante una ecuación del tipo y = m x + b, donde x, y son variables en un plano cartesiano. En dicha expresión m es denominada la "pendiente de la recta" y está relacionada con la inclinación que toma la recta respecto a un par de ejes que definen el plano, mientras que b es el denominado "término independiente" u "ordenada al origen" y es el valor de la ordenada del punto en el cual la recta corta al eje vertical en el plano.

    Índice

    1 Definiciones y postulados de Euclides relacionados con la recta

    2 Características de la recta

    2.1 Semirrecta

    2.2 Semirrecta opuesta

    3 Ecuación de la recta en el plano

    3.1 Pendiente y ordenada al origen

    3.1.1 Ejemplos

    3.2 Forma simplificada de la ecuación de la recta

    3.3 Forma segmentaria de la ecuación de la recta (ecuación simétrica)

    3.4 Ecuación general de la recta

    3.5 Ecuación normal de la recta (primera forma)

    3.6 Ecuación normal de la recta (segunda forma)

    3.7 Haz de rectas que pasan por un punto

    3.8 Recta que pasa por dos puntos

    3.9 Fórmulas para hallar "x" e "y" en una recta dada por coordenadas.

    3.10 Fórmulas para hallar el punto de intersección de dos rectas dadas por sus puntos de coordenadas.

    3.11 Recta que no pasa por el origen

    3.12 Rectas notables

    3.13 Rectas en el plano como espacio vectorial y afín

    3.13.1 Mediante dos puntos del plano afín

    3.13.1.1 Ejemplo

    3.13.2 Mediante un punto y un vector

    3.13.2.1 Ejemplo

    3.13.3 Rectas notables

    3.13.4 Rectas como producto escalar

    4 Ecuación de la recta en el espacio

    4.1 Recta determinada mediante un sistema de ecuaciones

    4.2 Recta determinada mediante vectores

    4.2.1 Posiciones relativas entre rectas

    5 Véase también 6 Notas 7 Referencias 8 Enlaces externos

    Definiciones y postulados de Euclides relacionados con la recta[editar]

    Euclides, en su tratado denominado 1​ establece varias definiciones relacionadas con la línea y la línea recta:

    Una línea es una longitud sin anchura (Libro I, definición 2).

    Los extremos de una línea son puntos (Libro I, definición 3).

    Una línea recta es aquella que yace por igual respecto de los puntos que están en ella (Libro I, definición 4).

    Características de la recta[editar]

    La recta se prolonga indefinidamente en ambos sentidos.

    En geometría euclidiana, la distancia más corta entre dos puntos es la línea recta.

    La recta puede definirse como el conjunto de puntos situados a lo largo de la intersección de dos planos.

    Semirrecta[editar]

    Haz de rayos.

    Se llama semirrectanota 1​ cada una de las dos partes en que queda dividida una recta al ser cortada en cualquiera de sus puntos. Es la parte de una recta conformada por todos los puntos que se ubican hacia un lado de un punto fijo de la recta, denominado , a partir del cual se extiende indefinidamente en un solo sentido.

    Semirrecta opuesta[editar]

    La semirrecta opuesta de una semirrecta es la otra semirrecta salida de la recta que define la primera.5​6​

    Cada semirrecta solo tiene una semirrecta opuestos.

    Una semirrecta y su semirrecta opuesta tienen el mismo origen.

    Ecuación de la recta en el plano[editar]

    En un plano cartesiano, podemos representar una recta mediante una ecuación general definida en dicho plano, ya sea mediante coordenadas usando puntos y vectores, o bien funciones que especifican dichas coordenadas.

    Pendiente y ordenada al origen[editar]

    Dada una recta mediante un punto,

    {\displaystyle P=(x_{0},y_{0})\,}

    , y una pendiente {\displaystyle m\,} :

    Se puede obtener la ecuación de la recta a partir de la fórmula de la pendiente (ecuación punto-pendiente):

    {\displaystyle y-y_{0}=m(x-x_{0})\!}

    donde {\displaystyle m}

    es la tangente del ángulo que forma la recta con el eje de abscisas X.

    Ejemplos[editar]

    a) La ecuación de la recta que pasa por el punto

    {\displaystyle A=(3,-5)}

    fuente : es.wikipedia.org

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    fuente : brainly.lat

    ¿Quieres ver la respuesta o más?
    Santiago 13 day ago
    4

    Chicos, ¿alguien sabe la respuesta?

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