Question

URGENTEEEEE

Os pontos A(a, 0), B(1, –2) e C(3, 2) são vértices de um triângulo. Então, necessariamente:

a) a = –1

b) a = –2

c) a = 2

d) a ≠ 2

e) a ≠ –2


Qual a equação geral da reta que passa pelos pontos A(1; 3) e B(2; –4)?

a) 7x + y – 7 = 0

b) x + 7y – 10 = 0

c) 7x + y – 10 = 0

d) 7x + y + 10 = 0

e) x + 7y + 10 = 0

Answer 1

1)

$\large\mathsf{\begin{bmatrix}a&0&1\\1&-2&1\\3&2&1\end{bmatrix}\ne0}$

$\mathsf{a(-2-2)+1(2+6)\ne0}\\\mathsf{-4a+8\ne0}$

$\mathsf{4a\ne8}\\\mathsf{a\ne\dfrac{8}{4}}$

$\mathsf{a\ne2}$

letra d

2)

A(1,3) e B(2,-4)

$\large\mathsf{\begin{bmatrix}1&3&1\\2&-4&1\\x&y&1\end{bmatrix}=0}$

$\mathsf{1(-4-y)-3(2-x)+1(2y+4x)=0}\\\mathsf{-4-y-6+3x+2y+4x=0}$

$\boxed{\boxed{\mathsf{7x+y-10=0}}}$

letra c