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Geometría Analítica ESO4

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Geometría Analítica ESO4

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Quiz de geometría analítica (4º ESO)

Created by

Elia Rodríguez Gallego
Elia Rodríguez Gallego
Spain

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Geometría Analítica ESO4
 

Geometría Analítica ESO4Online version

Quiz de geometría analítica (4º ESO)

by Elia Rodríguez Gallego
1

Dados los puntos A(2, -1) y B(-3, 4). ¿Cuál es la distancia AB?

2

La recta que pasa por P(1,2) y tiene pendiente m=3 tiene ecuación:

3

Si dos rectas son perpendiculares y una tiene pendiente m=2, la pendiente de la otra debe ser:

4

Halla la ecuación general de una recta que pasa por (0,4) y (2,0).

5

El punto medio de AB con A(-2,3) y B(6,-1) es:

6

La pendiente de la recta que pasa por A(4,0) y B(0,6) es:

7

La distancia entre A(1,2) y B(-3,5) es: (Módulo del vector)

8

La recta paralela a y=2x+3 que pasa por (0,0) tiene ecuación:

9

Las coordenadas del punto simétrico a A(-2,3) con respecto a B(5, 2) son

10

El vector director de la recta que pasa por P(1,2) y Q(4,6) es:

11

Los puntos A(1,-5), B(2,3) y C(3,11)

12

Los vectores AB= (-2,4) Y CD= (8, 4)

13

El valor de a para que los puntos A(5,3), B(1, -4) y C(a-1, 0) es:

14

La pendiente de la recta y=4 es

Explicación

La distancia es √[(Δx)^2+(Δy)^2] = √[(5)^2+( -5)^2] = √50.

Usa y=mx+b y pasa por (1,2): 2=3(1)+b → b=-1.

Rectas perpendiculares tienen la pendiente inversa y cambiada de signo

Calculo la pendiente a través del vector director de la recta y sustituyo en uno de los puntos.

Punto medio: ((x1+x2)/2,(y1+y2)/2) = ((4)/2, (2)/2) = (2,1).

m=(Δy)/(Δx)=(6-0)/(0-4)=6/(-4)=-3/2.

Para calcular la distancia entre dos puntos se calcula el modulo del vector

Si es paralela pasa tiene la misma pendiente y al pasar por el (0,0) la ordenada en el origen es 0

Consideramos a B como el punto medio

Vector director Q-P = (3,4).

Los puntos están alineados, pertenecen a la misma recta.

Hay que calcular los vectores AB y AC y hacerlos proporcionales

Recta paralela al eje OY, su pendiente es 0

 
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