Question

Os pontos A ( 4,5 ), B ( 7,5 ) e C ( 4,9 ) são vértices de um triângulo retângulo. A área desse triângulo é: *

a) 5 u.a

b) 6 u.a

c) 7 u.a

d) 8 u.a

e) 9 u.a​

Answer 1

$\boxed{S=\dfrac{1}{2}\left|\begin{array}{ccc}x_A&y_A&1\\x_B&y_B&1\\x_C&y_C&1\end{array}\right|}$

$A(x_A,y_A)=A(4,5)\\ B(x_B,y_B)=B(7,5)\\ C(x_C,y_C)=C(4,9)$

$S=\dfrac{1}{2}\left|\begin{array}{ccc}4&5&1\\7&5&1\\4&9&1\end{array}\right|\ \therefore$

$S=\dfrac{1}{2}\bigg(20+20+63-20-35-36\bigg)\ \therefore$

$S=\dfrac{12}{2}\ \therefore\ \boxed{S=6\ u.a.}$