Question

Se a distância do ponto P(0,p) à reta r, de equação 4x+3y-2=0, é igual a 2 unidades, determine a coordenada p.

Answer 1

Olá!!

Resolução!!

P ( 0, p ) e r : 4x + 3y - 2 = 0 D = 2

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D = | ax + by + c |/√a² + b²
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2 = | 4x + 3y - 2 |/√4² + 3²
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2 = | 4 • 0 + 3 • p - 2 |/√16 + 9

2 = | 0 + 3p - 2 |/√25

2 = | 3p - 2 |/5

2 = ( 3p - 2 )/5

( 3p - 2 )/5 = 2

MMC ( 5 ) = 5

( 3p - 2 )/5 = 2 • ( 5 )
( 15p - 10 )/5 = 10
3p - 2 = 10
3p = 10 + 2
3p = 12
p = 12/3
p = 4

Ou

- 2 = ( 3p - 2 )/5
( 3p - 2 )/5 = - 2

MMC ( 5 ) = 5

( 3p - 2 )/5 = - 2 • ( 5 )
( 15p - 10 )/5 = - 10
3p - 2 = - 10
3p = - 10 + 2
3p = - 8
p = - 8/3

Logo, p = 4 ou p = - 8/3

Espero ter ajudado;