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8. Dados los siguientes puntos \( K(3,2), L(6,5) \) y \( M(10,5) \). Que son los vértices de un triangulo, Encuentra los puntos medio de cada segmento de recta.

Ask by Huff Schofield. in Mexico
Mar 09,2025

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Los puntos medios de los segmentos son: - Entre \( K(3,2) \) y \( L(6,5) \): \( (4.5, 3.5) \) - Entre \( L(6,5) \) y \( M(10,5) \): \( (8, 5) \) - Entre \( M(10,5) \) y \( K(3,2) \): \( (6.5, 3.5) \)

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Para encontrar el punto medio de un segmento de recta, utilizamos la fórmula: \[ P_{m} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] 1. Para el segmento \( KL \): \[ P_{KL} = \left( \frac{3 + 6}{2}, \frac{2 + 5}{2} \right) = \left( \frac{9}{2}, \frac{7}{2} \right) = (4.5, 3.5) \] 2. Para el segmento \( LM \): \[ P_{LM} = \left( \frac{6 + 10}{2}, \frac{5 + 5}{2} \right) = \left( \frac{16}{2}, \frac{10}{2} \right) = (8, 5) \] 3. Para el segmento \( MK \): \[ P_{MK} = \left( \frac{10 + 3}{2}, \frac{5 + 2}{2} \right) = \left( \frac{13}{2}, \frac{7}{2} \right) = (6.5, 3.5) \] Por lo tanto, los puntos medios son: - Punto medio \( KL \): \( (4.5, 3.5) \) - Punto medio \( LM \): \( (8, 5) \) - Punto medio \( MK \): \( (6.5, 3.5) \)

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