Question

In raportul cartezian xOy, se considera punctele M(0, 2) N(6, 8) P(3, 5) .
a) Determinati ecuatia dreptei MN.
b) Aria ΔMOP.
c)Arata ca M,N,P sunt coliniare.

Answer 1

Punctul a

[tex] \left[\begin{array}{ccc}1&1&1\\x&0&6\\y&2&8\end{array}\right]=0 0+2x+6y-(0+12+8x)=0 2x+6y-12-8x=0 -6x+6y-12=0 /(-1) 6x-6y+12=0 / :6 x-y+2=0 [/tex]

Punctul b

$A= \frac{1}{2}*|delta|$

[tex]delta= \left[\begin{array}{ccc}1&1&1\\0&6&3\\2&8&5\end{array}\right] = 30+6+0-(12+24+0)=36-12-24=0[/tex]

$A= \frac{1}{2}*|0|=0$

Punctul c

$\left[\begin{array}{ccc}1&1&1\\0&6&3\\2&8&5\end{array}\right] = 30+6+0-(12+24+0)=36-12-24=0$

Punctele M,N,P sunt coliniare