Question

A) Quais as coodenadas dos vértices desse triângulo B) Qual a medida da mediana cm3 C) Quais as coordenadas do seu baricemento

Answer 1

a)

$\boxed{\begin{array}{c}\sf{As~coordenadas~s\tilde{a}o~A(0,0)~B(3,0)~e~C(0,-4)}\end{array}}$

b)

vamos calcular as coordenadas do ponto médio do segmento $\sf{\overline{BC}}$ :

$\sf{x_M=\dfrac{x_B+x_C}{2}=\dfrac{3+0}{2}=\dfrac{3}{2}}\\\sf{y_M=\dfrac{y_B+y_C}{2}=\dfrac{0-4}{2}=-\dfrac{4}{2}=-2}$

$\boxed{\begin{array}{c} \sf{As~coordenadas~do~ponto~m\acute{e}dio~s\tilde{a}o~M\left(\dfrac{3}{2},-2\right)}\\\sf{Vamos~calcular~a~dist\hat{a}ncia~do~ponto~A~ao~ponto~M}\end{array}}$

$\sf{d_{A,M}=\sqrt{\left(\dfrac{3}{2}\right)^2+(-2)^2}=\sqrt{\dfrac{9}{4}+4}}\\\sf{d_{A,M}=\sqrt{\dfrac{9+16}{4}}=\sqrt{\dfrac{25}{4}}=\dfrac{5}{2}~\checkmark}$

c)

$\sf{x_G=\dfrac{0+3+0}{3}=\dfrac{3}{3}=1}\\\sf{y_G=\dfrac{0+0-4}{3}=-\dfrac{4}{3}}$

$\boxed{\begin{array}{c}\sf{Portanto~as~coordenadas~do~baricentro~s\tilde{a}o~G\left(1,-\dfrac{4}{3}\right)}\end{array}}$