Harris Nunez
05/14/2023 · Junior High School
a Calcuten la distancia de la recta \( 3 x+4 y+75=0 \) al origen de coordenadas.
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Para calcular la distancia de la recta \( 3x + 4y + 75 = 0 \) al origen de coordenadas, podemos usar la fórmula de la distancia desde un punto \( (x_0, y_0) \) a una recta \( Ax + By + C = 0 \):
\[
d = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}
\]
En este caso, la recta está dada por \( A = 3 \), \( B = 4 \) y \( C = 75 \). El origen de coordenadas es el punto \( (0, 0) \), por lo que \( x_0 = 0 \) y \( y_0 = 0 \).
Sustituyendo estos valores en la fórmula:
\[
d = \frac{|3(0) + 4(0) + 75|}{\sqrt{3^2 + 4^2}} = \frac{|0 + 0 + 75|}{\sqrt{9 + 16}} = \frac{75}{\sqrt{25}} = \frac{75}{5} = 15
\]
Por lo tanto, la distancia de la recta \( 3x + 4y + 75 = 0 \) al origen de coordenadas es \( 15 \) unidades.
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La distancia de la recta \( 3x + 4y + 75 = 0 \) al origen es \( 15 \) unidades.
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