Răspuns:
Explicație pas cu pas:
AB = √[(-1 -1)^2 + (0 - 0)^2] = √4 = 2
AC = √[(0 - 1)^2 + (1 - 0)^2] = √2
BC = √[(0 + 1)^2 + (1 - 0)^2] = √2
P = AB + AC + BC = 2 + √2 + √2 = 2 + 2√2
p = P : 2 = (2 + 2√2) : 2 = 1 + √2
A = √p(p-a)(p-b)(p-c)
p(p-a)(p-b)(p-c) = (1 + √2)(1 + √2 - 2)(1 + √2 - √2)(1 + √2 - √2)
= (1 + √2)(√2 - 1)*1*1 = (√2 + 1)(√2 - 1) = 2 - 1 = 1
A = √1 = 1
A(1,0) B(-1,0) C(0,1)
Aria=1/2×|delta|
delta=|1 0 1|
|-1 0 1|
|0 1 1|
1 0 1
-1 0 1
=0-1+0-0-1-0
= -2
Aria= 1/2×|-2|
A=1/2×2
A=2/2
A=1
