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a. Sea \( Q(7,-2) \) determina las coordenadas del punto \( P(x, y) \) si \( M(5,12) \) es el punto medio del segmento \( P Q \).

Ask by Salinas Parsons. in Colombia
Mar 17,2025

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Las coordenadas del punto \( P \) son \( (3, 26) \).

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Para encontrar las coordenadas del punto \( P(x, y) \), utilizamos la fórmula del punto medio, que establece que las coordenadas del punto medio \( M \) son la media aritmética de las coordenadas de los extremos del segmento. Así, tenemos: \[ M_x = \frac{x_1 + x_2}{2} \quad \text{y} \quad M_y = \frac{y_1 + y_2}{2}. \] Dado que \( M(5,12) \) es el punto medio y \( Q(7,-2) \), podemos establecer las ecuaciones: \[ 5 = \frac{x + 7}{2} \quad \text{y} \quad 12 = \frac{y - 2}{2}. \] Resolviendo la primera ecuación: \[ 10 = x + 7 \implies x = 3. \] Ahora, resolviendo la segunda ecuación: \[ 24 = y - 2 \implies y = 26. \] Por lo tanto, las coordenadas del punto \( P \) son \( P(3, 26) \).

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