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Conceptos Clave

Línea Recta

Se cuenta con varias definiciones para la recta; cada una de estas definiciones tiene que ver con el contexto. La definición según la geometría euclidiana: "Una línea recta es aquella que yace por igual respecto de los puntos que están en ella"

En el caso de geometría analítica es la siguiente se puede definir como: "Una recta es el conjunto de todos los puntos del plano, donde las coordenadas de cada punto obedecen una relación de primer grado"

Aunque también se puede entender de la siguiente forma “La recta es el lugar geométrico de los puntos tales que, tomados dos cualesquiera del lugar geométrico, el valor de la pendiente siempre resulta constante.
Una linea

Geometría Analítica. (2021). Línea Recta. Recuperado de https://sites.google.com/site/ganalitica2011/modulo-1-linea-recta

Forma General de la Recta y su Pendiente

La Forma General La Recta es la relación entre dos variables X y Y a través de una igualdad, es decir, de una expresión matemática de primer grado que tiene la siguiente forma:

Ax+By+C=0

Donde A, B y C son números reales tales que A y B no son iguales a cero al mismo tiempo, dado que:

  • Si A = 0 entonces la ecuación general de la recta será de la forma y = r lo que significa que todos los puntos de esta recta tendrán la misma coordenada en el Eje Y, es decir, su gráfica será una recta totalmente horizontal.
  • Si B = 0 entonces la ecuación general de la recta será de la forma x = r lo que significa que todos los puntos de esta recta tendrán la misma coordenada en el Eje X y su gráfica será una recta totalmente vertical.

Para obtener la pendiente de cualquier recta que se encuentre expresada en su forma general simplemente se aplica lo siguiente:

m = -A / B

Así por ejemplo si tenemos una recta cuya ecuación en su forma general es: 7x + 5y - 14 = 0;

Se puede observar que A = 7 y que B = 5 por lo tanto su pendiente será; m = -7/5

Rectas Perpendiculares

Si las rectas s y r se encuentran en el plano, entonces estas rectas serán perpendiculares si el producto de las pendientes es igual a -1 :

producto pendiente

que también se puede ver como:    

pendientes 3

 Nota: las rectas perpendiculares en el plano siempre se cruzan en un único punto. Sin embargo, que las rectas se crucen no es suficiente para decir que las rectas son perpendiculares.

Rectas Paralelas y Perpendiculares(2020). Rectas paralelas y perpendiculares. Recuperado de https://www.montereyinstitute.org/courses/DevelopmentalMath/TEXTGROUP-9-14_RESOURCE/U13_L2_T3_text_final_es.html

Recuperación del aprendizaje

A continuación se te van a presentar algunas frases, tienes 30 segundos para decir si son verdaderas o falsas 

undefined
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