Question

5) (PUC) Os pontos A(3,1), B(4,-2) e C(x,7) são
colineares. O valor de x é igual a:
a) 1
b) 2
C) 5

d) 6​

Answer 1

Resposta:

resolução do problema letra

a) 1

Answer 2

$\left[\begin{array}{ccc}3&1&1\\4&-2&1\\x&7&1\end{array}\right] \left[\begin{array}{ccc}3&1\\4&-2\\x&7\end{array}\right] = 0\\\\\\4 \cdot 7 + x + 3 \cdot (-2) -(4 + 3 \cdot 7 -2x) = 0\\28 + x - 6 - (4 + 21 - 2x) = 0\\22+x-(25-2x) = 0\\22 + x - 25 + 2x = 0\\2x + x = 25 - 22\\2x + x = 3\\3x = 3\\x = \frac 33\\\boxed{x = 1}$