Question

Fie dreapta (d):ax+by+c=0, a,b,c, reale. Aratati ca dreapta d intersecteaza axa Ox intr-un punct A si in axa Oy intr-un punct B, amandoua diferite de origine.Calculati aria triunghiului AOB

Answer 1

ax + by + c = 0
intersectia cu axa OX : y = 0   ax + c = 0    x = -c/a    A(-c/a; 0)   ≠ O(0;0)
intersectia cu axaOY : x = 0    by + c = 0    y = -c/b    B(0;-c/b) ≠ O(0;0)
A Δ AOB = BO·OA /2 = (-c/b)·(-c/a) / 2 = c²/2ab