Question

Verifique em cada caso se os três pontos estão alinhados não, e calcule a área caso sejam vértices de um triângulo

a) A (-2,4) B (1,1) C (2,0)

b) A(4,5) B(0,0) C(5,4)

c) A(4,3) B(2,-1) C(2,9)

d) A(0,5) B(5,0) C(11,-5)

e) A(1,-1) B(-1,-5) C(-3,-9)

f) A(3,0) B(4,2) C(7,8)

g) A(1,2) B(-3,-2) C(2,5)

h) A(1,8) B(2,3) C(-5,2)

i) A(6,8) B(3,4) C(6,0)

j) A(1,-2) B(4,-2) C(1,2)


Ajudaaaa

Answer 1

Explicação passo-a-passo:

a) A (-2,4) B (1,1) C (2,0)

-2 4 1

1 1 1

2 0 1

D = -2 . 1 . 1 + 4 . 1 . 2 + 1 . 1 . 0 - (2 . 1 . 1 + 0 . 1 . (-2) + 1 . 1 . 4)

D = -2 + 8 + 0 - 2 + 0 - 4

D = 0

Alinhados

b) A(4,5) B(0,0) C(5,4)

4 5 1

0 0 1

5 4 1

D = 4 . 0 . 1 + 5 . 1 . 5 + 1 . 0 . 4 - (5 . 0 . 1 + 4 . 1 . 4 + 1 . 0 . 5)

D = 0 + 25 + 0 + 0 - 16 + 0

D = 9

A = 1/2 . |D|

A = 1/2 . 9

A = 9/2

c) A(4,3) B(2,-1) C(2,9)

4 3 1

2 -1 1

2 9 1

D = 4 . (-1) . 1 + 3 . 1 . 2 + 1 . 2 . 9 - (2 . (-1) . 1 + 9 . 1 . 4 + 1 . 2 . 3)

D = -4 + 6 + 18 + 2 - 36 - 6

D = -20

A = 1/2 . |D|

A = 1/2 . |-20|

A = 1/2 . 20

A = 20/2

A = 10

d) A(0,5) B(5,0) C(11,-5)

0 5 1

5 0 1

11 -5 1

D = 0 . 0 . 1 + 5 . 1 . 11 + 1 . 5 . (-5) - (11 . 0 . 1 + (-5) . 1 . 0 + 1 . 5 . 5)

D = 0 + 55 - 25 + 0 + 0 - 25

D = 5

A = 1/2 . |D|

A = 1/2 . |5|

A = 1/2 . 5

A = 5/2

e) A(1,-1) B(-1,-5) C(-3,-9)

1 -1 1

-1 -5 1

-3 -9 1

D = 1 . (-5) . 1 + (-1) . 1 . (-3) + 1 . (-1) . (-9) - (-3 . (-5) . 1 + (-9) . 1 . 1 + 1 . (-1) . (-1))

D = -5 + 3 + 9 - 15 + 9 - 1

D = 0

Alinhados

f) A(3,0) B(4,2) C(7,8)

3 0 1

4 2 1

7 8 1

D = 3 . 2 . 1 + 0 . 1 . 7 + 1 . 4 . 8 - (7 . 2 . 1 + 8 . 1 . 3 + 1 . 4 . 0)

D = 6 + 0 + 32 - 14 - 24 + 0

D = 0

Alinhados

g) A(1,2) B(-3,-2) C(2,5)

1 2 1

-3 -2 1

2 5 1

D = 1 . (-2) . 1 + 2 . 1 . 2 + 1 . (-3) . 5 - (2 . (-2) . 1 + 5 . 1 . 1 + 1 . (-3) . 2)

D = -2 + 4 - 15 + 4 - 5 + 6

D = -8

A = 1/2 . |D|

A = 1/2 . |-8|

A = 1/2 . 8

A = 8/2

A = 4

h) A(1,8) B(2,3) C(-5,2)

1 8 1

2 3 1

-5 2 1

D = 1 . 3 . 1 + 8 . 1 . (-5) + 1 . 2 . 2 - (-5 . 3 . 1 + 2 . 1 . 1 + 1 . 2 . 8)

D = 3 - 40 + 4 + 15 - 2 - 16

D = -36

A = 1/2 . |D|

A = 1/2 . |-36|

A = 1/2 . 36

A = 36/2

A = 18

i) A(6,8) B(3,4) C(6,0)

6 8 1

3 4 1

6 0 1

D = 6 . 4 . 1 + 8 . 1 . 6 + 1 . 3 . 0 - (6 . 4 . 1 + 0 . 1 . 6 + 1 . 3 . 8)

D = 24 + 48 + 0 - 24 + 0 - 24

D = 24

A = 1/2 . |D|

A = 1/2 . |24|

A = 1/2 . 24

A = 24/2

A = 12

j) A(1,-2) B(4,-2) C(1,2)

1 -2 1

4 -2 1

1 2 1

D = 1 . (-2) . 1 + (-2) . 1 . 1 + 1 . 4 . 2 - (1 . (-2) . 1 + 2 . 1 . 1 + 1 . 4 . (-2))

D = -2 - 2 + 8 + 2 - 2 + 8

D = 12

A = 1/2 . |D|

A = 1/2 . |12|

A = 1/2 . 12

A = 12/2

A = 6