Question

1) Verifique se as retas r e s são paralelas ou perpendiculares:

a) r : x + y – 5 = 0 e s: - x + y + 4 = 0
b) r: 3x – 2y + 1 = 0 e s : 6x – 4 y + 3 = 0
c) r: 3x + y -5 = 0 e s : 6x + 2y – 1 = 0
d) r: 3x – 2y + 1 = 0 e s: 2x + 3y – 2 = 0
e) r: 4x + 3y -1 = 0 e s : 6x – 8y + 5 = 0

Answer 1

Resposta:

a) r e s Perpendiculares

b) r e s Paralelas r //s

c) r e s Paralelas r //s

d) r e s Perpendiculares

e) r e s Perpendiculares

Explicação passo-a-passo:

a) x + y – 5 = 0 e s: - x + y + 4 = 0

r: x + y - 5 = 0

y = - x + 5

mr = - 1

s: - x + y + 4 = 0

y = x - 4

ms = 1

r e s são perpendiculares r _|_ s

b) r: 3x – 2y + 1 = 0 e s : 6x – 4 y + 3 = 0

r: 3x + 1= 2y

y = 3/2x + 1/2

mr = 3/2

s: 6x + 3 = 4y

y = 6x/4 + 3/4

y = 3x/2

ms = 3/2

mr = ms = 3/2 => São paralelas r // s

c) r: 3x + y -5 = 0 e s : 6x + 2y – 1 = 0

r: y = - 3x + 5

mr = - 3

s: 2y = - 6x + 1

y = - 6x/2 + 1/2

y = - 3x + 1/2

ms = - 3

mr = ms = - 3 (Paralelas)

d) r: 3x – 2y + 1 = 0 e s: 2x + 3y – 2 = 0

r: 2y = 3x + 1

y = 3x/2 + 1/2

mr = 3/2

s: 3y = - 2x + 2

y = - 2x/3 + 2/3

ms = - 2/3

r e s Perpendiculares

e) r: 4x + 3y -1 = 0 e s : 6x – 8y + 5 = 0

r: 3y = - 4x + 1

y = - 4x/3 + 1/3

mr = - 4/3

s: 8y = 6x + 5

y = 6x/8 + 5/8

y = 3x/4 + 5/8

ms = 3/4

r e s Perpendiculares