Question

Os pontos (1, 3), (2, 7) e (4, K) do plano cartesiano estão alinhados se e somente se K for igual a:

A) 11
B) 12
C) 13
D) 14
E) 15

Answer 1

Olá.

$\left\{\begin{array}{ccc}x_a&y_a&1\\x_b&y_b&1\\x_c&y_c&1\end{array}\right\}=0\\\\\\ \left|\begin{array}{ccc}x_a&y_a&1\\x_b&y_b&1\\x_c&y_c&1\end{array}\right|=0\\\\\\\left|\begin{array}{ccc}1&3&1\\2&7&1\\4&K&1\end{array}\right|=0\\\\\\\left|\begin{array}{ccc}1&3&1\\2&7&1\\4&K&1\end{array}\right|\left\begin{array}{ccc}1&3&\\2&7&\\4&K&\end{array}\right=0$

$(1\cdot7\cdot1+3\cdot1\cdot4+1\cdot2\cdot K)-(4\cdot7\cdot1+K\cdot1\cdot1+1\cdot2\cdot3)=0\\(7+12+2K)-(28+K+6)=0\\(19+2K)-(34+K)=0\\19+2K-34-K=0\\K-15=0\\\\\boxed{\boxed{K=15}}$


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