Răspuns:
Explicație pas cu pas:
(a)
A(0,5), B(3,1), C(3,9)
P= AB + BC + AC.
AB=[(3-0)^2 + (1-5)^2]^1/2=
=[3^2 + (-4)^2]^1/2=
=(9+16)^1/2=25^1/2=5.
BC=[(3-3)^2 + (9-1)^2]^1/2=
=[0 + 8^2]^1/2=
=(8^2)^1/2=8
AC=[(3-0)^2 + (9-5)^2]^1/2=
=[3^2 + (4)^2]^1/2=
=(9+16)^1/2=25^1/2=5
Deci P=5 + 8 +5=18
(b) D(1,6), E(6,-6), F(6,6)
P= DE + EF + DF
DE=[(6-1)^2 + (-6-6)^2]^1/2=
=[5^2 + (-12)^2]^1/2=
=(25 + 144 )^1/2=129^1/2=13
EF={(6-6)^2 + [6-(-6)]^2]^1/2=
=(0+ 12^2)^1/2=
=144^1/2=12
DF=[(6-1)^2 + (6-6)^2]^1/2=
=[6^2 + 0^2]^1/2=
=(6^2)^1/2=6
Deci P= 13 + 12 +6 = 31.
(c) M(3,3), N(-5,-5), P(7,7)
Se observa ca cele trei puncte au fiecare abscisa egala cu ordonata (adica x cu y), deci ele se afla pe aceeasi linie, data de y=x. Asadar punctele nu formează un triunghi.
