Question

Determine as retas suportes dos lados de um triangulo cujos vértices são os pontos A(-2,1) B(0,3) e C(2,0).

Answer 1

Reta AB:

m(AB) = (Ya - Yb)/(Xa - Xb)
m(AB) = (1 - 3)/(-2 - 0)
m(AB) = -2/-2 = 1

Y - Yb = m·(X - Xb)
Y - 3 = X
Y - X - 3 = 0←

Reta AC:

m(AC) = (Ya - Yc)/(Xa - Xc)
m(AC) = (1 - 0)/(-2 - 2)
m(AC) = -1/4

Y - Ya = m·(X - Xa)
Y - 1 = -1/4·[X - (-2)]
Y = (-X - 2)·1/4 + 1
Y = (-X - 2 + 4)·1/4
4Y = -X +2
X + 4Y - 2 = 0 ←

Reta BC:

m(BC) = (Yb - Yc)/(Xb - Xc)
m(BC) = (3 - 0)/(0 - 2)
m(BC) = -3/2

Y - Yb = m·(X - Xb)
Y - 3 = -3X/2
Y = -3X/2 + 3
2Y = -3X + 6
3X + 2Y - 6 = 0 ←