Question

Determine o ponto T, pertencente ao eixo 0y, que dista igualmente dos pontos A (2,3) e B (6,5)

Answer 1

Olá!!

Resolução!!

A ( 2, 3 ), T ( x, 0 ) e B ( 6, 5 )

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AT = √( x2 - x1 )² + ( y2 - y1 )²
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AT = √( x - 2 )² + ( 0 - 3 )²
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AT = (√( x - 2 )² + ( 0 - 3 )²)²
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AT = ( x - 2 )² + ( 0 - 3 )²
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AT = ( x )² - 2 • x • 2 + 2² + ( - 3 )²
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AT = x² - 4x + 4 + 9
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AT = x² - 4x + 13

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BT = √( x2 - x1 )² + ( y2 - y1 )²
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BT = √( 6 - x )² + ( 5 - 0 )²
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BT = (√( 6 - x )² + ( 5 - 0 )²)²
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BT = ( 6 - x )² + ( 5 - 0 )²
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BT = 6² - 2 • 6 • x + ( x )² + 5²
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BT = 36 - 12x + x² + 25
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BT = 61 - 12x + x²

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AT = BT
x² - 4x + 13 = 61 - 12x + x²
x² - 4x + 13 - 61 + 12x - x² = 0
x² - x² + 12x + 4x - 61 + 13 = 0
16x = - 48
x = - 48/16
x = - 3

Logo, o ponto T é ( - 3, 0 )

Espero ter ajudado!!!