Question

Os pontos (6,a), (3,2) e (0, b) estão alinhados, então: a) a-b=2 b) a+2b c) a/b = 3/2 d) a+b=4 e) a-b=4

Answer 1

$Sabemos \ que: \\\\ A=(6,a), \ B=(3,2) \ e \ C=(0, b) \ --\ \textgreater \ \ colineares \\ m_{AB}=m_{AC}=m_{BC} \ --\ \textgreater \ \ coeficiente \ angular \ da \ reta \\ m= \frac{\Delta y}{\Delta x} \\\\ Logo: \\\\ m_{AB}=m_{AC} \\\\ \frac{y_B-y_A}{x_B-x_A}= \frac{y_C-y_A}{x_C-x_A} \\\\ \frac{2-a}{3-6}= \frac{b-a}{0-6} \ --\ \textgreater \ \ \frac{2-a}{-3}=\frac{b-a}{-6} \\\\ -6(2-a)=-3(b-a) \ --\ \textgreater \ \ -12+6a=-3b+3a \\\\ 6a+3b-3a=12 \ --\ \textgreater \ \ 3a+3b=12 \\\\ 3(a+b)=12 \ --\ \textgreater \ \ a+b=4$

Resposta: Alternativa D