Question

Qual deve ser o valor de X para que os pontos PQR, P = (1, 1), Q = (6, X) e R = (3, 5), no plano cartesiano estejam aninhados.
1 ponto
A) - 10.
B) 10.
C) 11.
D) -3.
E) 3.​

Answer 1

$\boxed{\begin{array}{l}\sf sejam~A(x_A, y_A), B(x_B, y_B)~e~C(x_C, y_C)~pontos~quaisquer~do~plano~cartesiano.\\\sf dizemos~que~est\tilde ao~alinhados~quando:\\\begin{vmatrix}\sf x_A&\sf y_A&\sf1\\\sf x_B&\sf y_B&\sf1\\\sf x_C&\sf y_C&\sf1\end{vmatrix} =0\end{array}}$

$\purple{\boxed{\begin{array}{l}\begin{vmatrix} \sf1&\sf1&\sf1\\\sf6&\sf x&\sf1\\\sf3&\sf5&\sf1\end{vmatrix}=0\\\sf1\cdot(x-5)-1\cdot(6-3)+1\cdot(30-3x)=0\\\sf x-5-3+30-3x=0\\\sf x-3x=-30+5+3\\\sf-2x=-22\cdot(-1)\\\sf 2x=22\\\sf x=\dfrac{22}{2}\\\sf x=11\green{\checkmark}\end{array}}}$