Question

os pontos A(1 , 2) , B (x , 0) e C(3 ,4) são colineares , então o valor de x é :
a) ( ) x=0
b) ( ) x=2
c) ( ) x=-3
d) ( ) x=-1
e) ( ) x=-5

Answer 1

$Sabemos \ que: \\\\ A=(1 , 2) \ \| \ B = (x , 0) \ \| \ C= (3 ,4) \\ m_{AC}=m_{AB}=m_{BC} \ -\ \textgreater \ coeficiente \ angular \ da \ reta \\\\ Logo: \\\\ m_{AC}=m_{AB} \\\\ \frac{y_C-y_A}{x_C-x_A}= \frac{y_B-y_A}{x_C-x_A} \\\\ \frac{4-2}{3-1}= \frac{0-2}{x-1} \\\\ \frac{2}{2}= \frac{-2}{x-1} \\\\ x-1=-2 \\\\ x=-2+1 \\\\ x=-1 \\\\ Alternativa \ D.$