Observa el plano y determina la distancia entre el par de puntos indicados en cadacaso.
Respuestas
Primero se deben obtener las coordenadas de cada par ordenado o punto.
A(-4,5)
B(3,4)
C(-2,1)
D(1,1)
E(4,-2)
F(-4,-3)
G(0,-4)
Con estos se puede calcular las distancias solicitadas a partir de la fórmula siguiente:
d(a,b) = √[(x₂ – x₁)² + (y₂ – y₁)²]
Resolviendo:
a) d(A,B)
d(A,B) = √[(3 – (- 4))² + (4 – 5)²] = √[(3 + 4)² + (4 – 5)²] = √[(7)² + (- 1)²] = √(49 + 1) = √50 = 7,0710
d(A,B) = 7,0710
b) d(A,C)
d(A,C) = √[((- 2) – (- 4))² + (1 – 5)²] = √[(-2 + 4)² + (1 – 5)²] = √[(2)² + (- 4)²] = √(4 + 16) = √20 = 4,4721
d(A,C) = 4,4721
c) d(B,F)
d(B,F) = √[(3 – (- 4))² + ((- 3) – 5)²] = √[(3 + 4)² + (- 3 – 5)²] = √[(7)² + (-8)²] = √(49 + 64) = √113 = 10,6301
d(B,F) = 10,6301
d) d(A,G)
d(A,G) = √[(0 – (- 4))² + ((- 4) – 5)²] = √[(0 + 4)² + (- 4 - 5)²] = √[(4)² + (- 9)²] = √(16 + 81) = √97 = 9,8488
d(A,G) = 9,8488
e) d(D,A)
d(D,A) = √[((- 4) – (1))² + (5 – 1)²] = √[(- 4 - 1)² + (4 – 5)²] = √[(- 5)² + (1)²] = √(25 + 1) = √26 = 5,0990
d(D,A) = 5,0990
f) d(A,E)
d(A,E) = √[(4 – (- 4))² + ((- 2) – 5)²] = √[(4 + 4)² + (-2 - 5)²] = √[(8)² + (- 7)²] = √(64 + 49) = √113 = 10,6301
d(A,E) = 10,6301
g) d(A,F)
d(A,F) = √[((-4) – (- 4))² + ((- 3) - 5)²] = √[(- 4 + 4)² + (- 3 – 5)²] = √[(0)² + (- 8)²] = √(0 + 64) = √64 = 8
d(A,F) = 8
h) d(B,D)
d(B,D) = √[(1 – 3)² + (1 – 4)²] = √[(- 2)² + (- 3)²] = √(4 + 9) = √13 = 3,0655
d(B,D) = 3,0655
i) d(C,D)
d(C,D) = √[(1 – (- 2))² + (1 – 1)²] = √[(1 + 2)² + (0)²] = √[(3)² = √9 = 3
d(C,D) = 3
Respuesta:
Explicación paso a paso:
Primero se deben obtener las coordenadas de cada par ordenado o punto.
A(-4,5)
B(3,4)
C(-2,1)
D(1,1)
E(4,-2)
F(-4,-3)
G(0,-4)
Con estos se puede calcular las distancias solicitadas a partir de la fórmula siguiente:
d(a,b) = √[(x₂ – x₁)² + (y₂ – y₁)²]
Resolviendo:
a) d(A,B)
d(A,B) = √[(3 – (- 4))² + (4 – 5)²] = √[(3 + 4)² + (4 – 5)²] = √[(7)² + (- 1)²] = √(49 + 1) = √50 = 7,0710
d(A,B) = 7,0710
b) d(A,C)
d(A,C) = √[((- 2) – (- 4))² + (1 – 5)²] = √[(-2 + 4)² + (1 – 5)²] = √[(2)² + (- 4)²] = √(4 + 16) = √20 = 4,4721
d(A,C) = 4,4721
c) d(B,F)
d(B,F) = √[(3 – (- 4))² + ((- 3) – 5)²] = √[(3 + 4)² + (- 3 – 5)²] = √[(7)² + (-8)²] = √(49 + 64) = √113 = 10,6301
d(B,F) = 10,6301
d) d(A,G)
d(A,G) = √[(0 – (- 4))² + ((- 4) – 5)²] = √[(0 + 4)² + (- 4 - 5)²] = √[(4)² + (- 9)²] = √(16 + 81) = √97 = 9,8488
d(A,G) = 9,8488
e) d(D,A)
d(D,A) = √[((- 4) – (1))² + (5 – 1)²] = √[(- 4 - 1)² + (4 – 5)²] = √[(- 5)² + (1)²] = √(25 + 1) = √26 = 5,0990
d(D,A) = 5,0990
f) d(A,E)
d(A,E) = √[(4 – (- 4))² + ((- 2) – 5)²] = √[(4 + 4)² + (-2 - 5)²] = √[(8)² + (- 7)²] = √(64 + 49) = √113 = 10,6301
d(A,E) = 10,6301
g) d(A,F)
d(A,F) = √[((-4) – (- 4))² + ((- 3) - 5)²] = √[(- 4 + 4)² + (- 3 – 5)²] = √[(0)² + (- 8)²] = √(0 + 64) = √64 = 8
d(A,F) = 8
h) d(B,D)
d(B,D) = √[(1 – 3)² + (1 – 4)²] = √[(- 2)² + (- 3)²] = √(4 + 9) = √13 = 3,0655
d(B,D) = 3,0655
i) d(C,D)
d(C,D) = √[(1 – (- 2))² + (1 – 1)²] = √[(1 + 2)² + (0)²] = √[(3)² = √9 = 3
d(C,D) = 3
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