GEOMETRIA ANALITICA Tema: Resolución de exámen.

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P = Formula pendiente[pic 75][pic 74]

Y – y1 = p (x – x1) F. punto pendiente[pic 76]

Medianas AB:

P.m. x (3/2) p.m. y (-2) c (-1,2)

P= = - [pic 77][pic 78]

Y – (-2) = -8/5 (x – 3/2) = 8/5x + y = 2/5

Medianas AC:

p.m. x (-1/2) p.m. y (-1/2) B (3,-1)

p = = - [pic 79][pic 80]

y – (-1/2) = -2/14 (x – ½) = 2/14x + y = -3/7

Medianas BC:

p.m. x (1) p.m. y (1/2) A (0, -3)

p = = - [pic 81][pic 82]

y – (1/2) = - 7/2 (x – 1) = 7/2x + y = 4

PUNTO DE INTERSECCION (BARICENTRO):

8/5x + y = 2/5

7/2x – y = 3[pic 83]

51/10x = 17/5

X = = ( ,- [pic 84][pic 85][pic 86][pic 87]

8/5 (170/255) + y = 2/5

16/15 + y = 2/5

Y= 2/5 – 16/15 = -2/3

- ECUACIONES DE LAS ALTURAS Y SU INTERSECCION.

X = y = Formula punto medio (x, y).[pic 90][pic 88][pic 89]

P = p∟ = - Pendiente perpendicular[pic 93][pic 91][pic 92]

Y – y1 = p∟ (x – x1) Formula punto pendiente.[pic 94]

Alturas AB:

p.m. x (3/2) p.m. y (1)

p = = 2/3 p∟ = -3/2[pic 95]

C (-1,2)

Y – 2= -3/2 (x – (-1) = 3/2x + y = 1/2

Alturas AC:

p.m. x (-1/2) p.m. y (-1/2)

p = = - p∟ = [pic 96][pic 97][pic 98]

B (3, -1)

Y – (-1) = 1/5 (x – 3) = 1/5x – y = 8/5

Alturas BC:

p.m. x (1) p.m. y (1/2)

p= = - p∟ = [pic 99][pic 100][pic 101]

A (0, -3)

Y1 – (-3) = 4/3 (x – 0)= 4/3x – y = 3

PUNTO DE INTERSECCION DE LAS ALTURAS (ORTOCENTRO)

4/3x – y = 3

3/2x + y = ½[pic 102]

17/6x = 7/2

X = = [pic 103][pic 104]

() + y = ½ (,- )[pic 105][pic 106][pic 107][pic 108]

+ y = ½[pic 109]

Y = ½ - = -[pic 110][pic 111]

- Ecuaciones de bisectrices sus puntos de intersección, así como la ecuación de la circunferencia inscrita.

[pic 112]

= F. para la bisectriz[pic 113][pic 114]

AX + BY = C Fórmula para los lados[pic 115]

AB Y AC:

= [pic 116][pic 117]

+ ) ( - ) = + )[pic 118][pic 119][pic 120][pic 121][pic 122][pic 123]

AC Y BC:

= [pic 124][pic 125]

(+ ) ( + ) = ( - )[pic 126][pic 127][pic 128][pic 129][pic 130][pic 131]

AB Y BC:

= [pic 132][pic 133]

( + ) ( - ) = ( + )[pic 134][pic 135][pic 136][pic 137][pic 138][pic 139]

Punto de intersección de bisectrices:

(x - + ( - ) = ( - )[pic 140][pic 141][pic 142][pic 143][pic 144][pic 145]

( + ) + ( - ) = ( + )[pic 146][pic 147][pic 148][pic 149][pic 150][pic 151]

(-15.27 – 25) + (-20.36 – 5) = (-25.45 + 15)

(-10.8 + 10) + (-14.4 -15) = (-18 + 45)

-40.27x – 25.36y = -10.45

-.08x – 29.4y = 27[pic 152]

-25.36y = -10.45

14799.225y = -12591.125[pic 153]

14773.865y = -13604.575

Y = = -0.920854157[pic 154]

-40.27x 25.36 (-0.920854157) = -10.45

-40.27x = -10.45 – 23.35279582

X = = 0.839403919[pic 155]

Circunferencia inscrita:

[pic 156]

= Fórmula para c.f.a. inscrita[pic 157]

= [pic 158][pic 159]

(x-0.839403919)^2 + (y+0.920854157) ^2 = (1.266286025) ^2

- Hallar la recta de Euler para el triángulo dado.

CIRCUCENTRO