Question

Dado o ponto p(3,2), determine a distância de p até a reta r, nos seguintes casos:

A) r:3x + 4y + 1= 0
B) r: x : 2+ y : 3 =1
C) r: y = 6
D) r: x = - 1
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Answer 1

Vamos là.

ponto P(3,2)

distancia do ponto(x0,y0) a reta Ax + By + C = 0  

d = |Ax0 + By0 + C|/√(A² + B²)

A) 3x + 4y + 1 = 0

A = 3, B = 4, C = 1, x0 = Px = 3, y0 = Py = 2

d = |Ax0 + By0 + C|/√(A² + B²)

d = |3*3 + 4*2+ 1|/√(3² + 4²)

d = l9 + 8 + 1l/5 = 18/5

B) x/2 + y/3 - 1 = 0

A = 1/2, B = 1/3, C = -1, x0 = 3, y0 = 2

d = |Ax0 + By0 + C|/√(A² + B²)

d = |3/2 + 2/3 -1|/√(1/4 + 1/9)

d = l7/6l/(√13/6) = 7√13/13

C) y = 6

A = 0, B = 6, C = 0, x0 = 3, y0 = 2

d = |Ax0 + By0 + C|/√(A² + B²)

d = | 6*2 |/√(6²) = 2

D) x = -1

A = -1, B = 0, C = 0, x0 = 3, y0 = 2

d = |Ax0 + By0 + C|/√(A² + B²)

d = |-1*3 |/√(1)² = 3