Question

Sabendo que os pontos A, B e C estão alinhados, determine o valor de m em função de n.
A) A(2,3) B ( -2,1) C ( 3,1)
B) A( 3,5) B( -2,1) C (M,N)
C) A(m,n) B ( -1,-1) C ( 4,1)

Answer 1

b)

$\begin{bmatrix}3&5&1\\-2&1&1\\m&n&1\end{bmatrix}=0$

$3(1-n)-5(-2-m)+1(-2n-m)=0\\3-3n+10+5m-2n-m=0\\5m-m=3n+2n-3-10\\4m=5n-13$

$\mathsf{m=\dfrac{5n-13}{4}}$

c)

$\begin{bmatrix}m&n&1\\-1&-1&1\\4&1&1\end{bmatrix}=0$

$m(-1-1)-n(-1-4)+1(-1+4)=0\\-2m+5n+3=0\\2m=5n+3$

$\mathsf{m=\dfrac{5n+3}{2}}$