Question
In the rectilinear path of a road described by the equation L: 3x +4y -5 = 0, a public telephone is located at Q. If a person is at point P(12;6), calculate the distance in meters to make the call.
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Answer to a math question In the rectilinear path of a road described by the equation L: 3x +4y -5 = 0, a public telephone is located at Q. If a person is at point P(12;6), calculate the distance in meters to make the call.
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4.492 Answers
1. Reemplace \( x \) y \( y \) en la ecuación del plano \( 3x + 4y - 5 = 0 \) con las coordenadas del punto \( P(12, 6) \):
d = \frac{|3(12) + 4(6) - 5|}{\sqrt{3^2 + 4^2}}
2. Simplifique la expresión para numerador:
- Calcule \( 3(12) + 4(6) - 5 \):
36 + 24 - 5 = 55
3. Simplifique la expresión para the denominador:
- Calcule \( \sqrt{3^2 + 4^2} \):
\sqrt{9 + 16} = \sqrt{25} = 5
4. Calcule el resultado final:
\frac{|55|}{5} = \frac{55}{5} = 11
5. La distancia desde el punto \( P \) a la línea es \( d = 11 \) metros
2. Simplifique la expresión para numerador:
- Calcule \( 3(12) + 4(6) - 5 \):
3. Simplifique la expresión para the denominador:
- Calcule \( \sqrt{3^2 + 4^2} \):
4. Calcule el resultado final:
5. La distancia desde el punto \( P \) a la línea es \( d = 11 \) metros
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