Question

Dados A(-1,-1),B(2,-1) e C(2,3), vertices de um triângulo,determine:
A)distancia do lado AC
B)O ponto medio do lado BC
C)O baricentro do triângulo ABC
D)represente graficamente o triângulo ABC

Answer 1

Olá,
Olá Beatriz, vamos lá:

Distância de AC:

$d_{\alpha\beta}= \sqrt{(x-x_o)^2+(y-y_o)^2}\\\\ d_{AC}= \sqrt{[2-(-1)]^2+[3-(-1)]^2}\\\\ d_{AC}= \sqrt{(2+1)^2+(3+1)^2}\\\\ d_{AC}= \sqrt{3^2+4^2}\\\\ d_{AC}= \sqrt{9+16}\\\\ d_{AC}= \sqrt{25}\\\\ \huge\boxed{d_{AC}=5}$


Ponto médio de BC:

$p_{m}= \left(\dfrac{x_a+x_b}{2}, \dfrac{y_a+y_b}{2}\right)\\\\ p_{m}=\left( \dfrac{2+2}{2}, \dfrac{-1+3}{2}\right)\\\\ p_{m}=\left( \dfrac{4}{2}, \dfrac{2}{2}\right)\\\\\\ \huge\boxed{p_{m}=(2,1)}$


Baricentro do triângulo ABC:

$\text{G}_{x,y}=\left( \dfrac{x_a+x_b+x_c}{3}, \dfrac{y_a+y_b+y_c}{3} \right)\\\\ \text{G}_{x,y} =\left( \dfrac{-1+2+2}{3}, \dfrac{-1+(-1)+3}{3}\right)\\\\ \text{G}_{x,y}=\left( \dfrac{3}{3}, \dfrac{3}{3} \right)\\\\\\ \huge\boxed{\text{G}_{x,y}=(1,1) }$


A representação gráfica está em anexo. Tenha ótimos estudos ;P