Дан треугольник ABC. AM – медиана треугольника. Если A (3; –6), B (4; 5), C (

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July 2022 1 9 Report

Дан треугольник ABC. AM – медиана треугольника. Если A (3; –6), B (4; 5), C (–2; 7), найди координаты вектора АМ

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mathkot

Ответ:

$\boxed{AM = \sqrt{148}} }$

Объяснение:

Так как точка M середина отрезка BC, то координаты точки $M(x_{m};y_{m})$ .

По формуле $M(x_{m};y_{m}) = (\frac{X_{B} + X_{C}}{2} ;\frac{Y_{B} + Y_{C}}{2} ) = (\frac{4 - 2}{2} ;\frac{5 + 7}{2} ) = (\frac{2}{2};\frac{12}{2} ) = M(1;6)$ .

Длинна AM по формуле:

$AM = \sqrt{(X_{M} - X_{A})^{2} + (Y_{M} - Y_{A})^{2}} = \sqrt{(1 - 3)^{2} + (6+6)^{2}}=\sqrt{(-2)^{2} + (12)^{2}} =$

$\sqrt{4 + 144} = \sqrt{148}$ .

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