Question

Se dau punctele A(3;1) B(-1;5) C(0;-2) in sistemul ortogonal de axe xOy
a) Aflati coordonatele mijlocului M al segmentului AB
b) Aflati aria triunghiului ABC ​​

Answer 1

Răspuns:

a) M(1,3); b) 12 u.m.²

Explicație pas cu pas:

A(3;1) ; B(-1;5) ; C(0;-2)

a)

$M(x_{M} ;y_{M})$

$x_{M} = \frac{x_{A} + x_{B}}{2} = \frac{3 + ( - 1)}{2} = \frac{2}{2} = 1 \\ </p><p>y_{M} = \frac{y_{A} + y_{B}}{2} = \frac{1 + 5}{2} = \frac{6}{2} = 3 \\ \implies M(1 ;3)$

b)

$\mathcal{A}_{\triangle ABC} = \frac{1}{2} \cdot |\Delta|$

$\Delta = \left|\begin{array}{ccc}3&1&1\\ - 1&5&1\\0& - 2&1\end{array}\right| = 3 \cdot 7 - 1 \cdot ( - 1) + 1 \cdot 2 = \\ = 21 + 1 + 2 = 24$

$\mathcal{A}_{\triangle ABC} = \frac{1}{2} \cdot |24| = 12 \ {u.m.}^{2}$