Question

3- A distância do ponto A(3,-5) e B(b,1)é igual a 13. Calcule o valor da abscissa b.

Answer 1

Olá!!

Resolução!!

A ( 3, - 5 ) , B ( b, 1 ) e AB = 13

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AB = √( x2 - x1 )² + ( y2 - y1 )²
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13 = √( 3 - b )² + ( 1 - ( - 5 ))²
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13 = √( 3 - b )² + ( 1 + 5 )²
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13² = (√( 3 - b )² + ( 1 + 5 )²)²

169 = ( 3 - b )² + ( 1 + 5 )²
169 = 3² - 2 • 3 • b + ( b )² + 6²
169 = 9 - 6b + b² + 36
9 - 6b + b² + 36 = 169
b² - 6b + 36 + 9 - 169 = 0
b² - 6b - 124 = 0 → Eq. do 2° grau

a = 1, b = - 6, c = - 124

∆ = b² - 4ac
∆ = ( - 6 )² - 4 • 1 • ( - 124 )
∆ = 36 + 496
∆ = 532

b = - b ± √∆ / 2a
b = - ( - 6 ) ± √532 / 2 • 1

532 | 2
266 | 2
133 | 7
19 | 19
1

√532 → √2² • 133 → 2 • √133 → 2√133

b = 6 ± 2√133/2
b' = 6 + 2√133/2
b' = 3 + √133
b" = 6 - 2√133/2
b" = 3 - √133

b = 3 - √133 ou b = 3 + √133

Logo, A abscissa b é ( 3 - √133, 1 ) ou ( 3 + √133, 1 )

Espero ter ajudado!!