Question

Fie triunghiul ABC cu vârfurile A(-4,0), B(1,5) și C(2,-2). Dacă punctul D este mijlocul laturii [AB] să se calculeze aria triunghiului BCD.​

Answer 1

Explicație pas cu pas:

$D\bigg(- \dfrac{3}{2} ; \dfrac{5}{2}\bigg)$

$\mathcal{A}_{\triangle BCD} = \dfrac{1}{2} \cdot |\Delta|$

$\left|\begin{array}{ccc}1&5&1\\2&-2&1\\- \dfrac{3}{2}&\dfrac{5}{2}&1\end{array}\right| = 1 \times \left|\begin{array}{ccc}-2&1\\\dfrac{5}{2}&1\end{array}\right| - 5 \times \left|\begin{array}{ccc}2&1\\- \dfrac{3}{2}&1\end{array}\right| + 1 \times \left|\begin{array}{ccc}2&-2\\- \dfrac{3}{2}&\dfrac{5}{2}\end{array}\right| =$

$= - 2 - \dfrac{5}{2} - 5\Big(2 + \dfrac{3}{2}\Big) + 5 - 3 = - 2 - \dfrac{5}{2} - 10 - \dfrac{15}{2} + 2 = - 10 - \dfrac{20}{2} = - 10 - 10 = - 20$

$\mathcal{A}_{\triangle BCD} = \dfrac{1}{2} \cdot |\Delta| = \dfrac{1}{2} \cdot | - 20| = \dfrac{1}{2} \cdot 20 = \bf 10$