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Quiz de Geometría Analítica: Rectas

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Quiz de Geometría Analítica: Rectas

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Ecuaciones y pendientes

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jindech gaitan
jindech gaitan
Panama

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Quiz de Geometría Analítica: Rectas
 

Quiz de Geometría Analítica: RectasOnline version

Ecuaciones y pendientes

by jindech gaitan
1

¿Qué ecuación es la forma punto-pendiente de una recta con pendiente m que pasa por (x1,y1)?

2

¿Cuál es la forma punto-pendiente de la recta que pasa por (3, -2) con pendiente 5?

3

La recta con pendiente m=2 que pasa por (0,4) en forma pendiente-intercepto es:

4

¿Qué representa la ordenada en el origen en una recta?

5

Ecuacion en forma general de una recta que pasa por (1,2) y tiene pendiente 3 es:

6

¿Qué forma corresponde a y = mx + b?

7

Si una recta tiene la ecuación general 2x + 3y - 6 = 0, ¿cuál es su pendiente m?

8

¿Qué condición describe la ecuación en forma punto-pendiente para una recta que pasa por (0, -5) con pendiente 4?

9

Convertir a forma general: de y = 3x + 7 a forma general Ax + By + C = 0 es:

10

¿Qué describe la ecuación Ax + By + C = 0?

Explicación

La forma correcto es y - y1 = m(x - x1). Las otras no representan la forma punto-pendiente.

Sustituyendo x1=3, y1=-2 resulta y+2=5(x-3).

Al pasar por (0,4) el intercepto y0 es 4, por eso y=2x+4.

La ordenada en el origen es el valor de y cuando x=0, es decir el intercepto b.

Sustituye en y - y1 = m(x - x1) y reordena a Ax + By + C = 0.

Y = mx + b es la forma pendiente-intercepto (y-intercepto b).

Para Ax+By+C=0, m = -A/B; aquí m = -2/3.

Sosteniendo x1=0, y1=-5, se obtiene y - (-5) = 4(x - 0) -> y + 5 = 4x.

Reorganiza: y = 3x + 7 -> -3x + y - 7 = 0.

La forma general es Ax + By + C = 0.

 
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