Question

Coordonate carteziene A(1,1) B(3,2) C(m,3) D eterminati valoarea numarului m stiind ca punctele A,B,C sunt coliniare

Answer 1

f(x) = ax + b 
A(1,1) ∈ Gf
=> f(1) = 1
a + b = 1
a = 1 - b

B(3,2) ∈ Gf
=> f(3) = 2
3a + b = 2
3(1-b) + b = 2
3 - 3b + b = 2
3 - 2b = 2
-2b = 2 - 3
-2b = -1 |·(-1)
2b = 1
b = 1 : 2

a = 1 - b = 1 - 1 : 2 
=> a = 1 : 2

C(m,3) ∈ Gf
=> f(m) = 3
a·m + b = 3
1 : 2 · m + 1 : 2 = 3
m : 2   = 3 - 1 : 2
m : 2 = (6-1) : 2
m : 2 = 5 : 2  |·2
m = 5