Question

Determine a equaçao geral da reta que passa pelo ponto
a) A (-1,2) B (2,3)
b) A (4,5) B (0,1)
c) A (2,-1) B (1,2)
d) A (3,5) B (2,-3)

Answer 1

a) A (-1,2) B (2,3)
y-y0=m(x-x0)
m=yA-yB/xA-XB
m=2-3/-1-2=-1/-3=1/3
m=1/3
y-y0=m(x-x0)
y-2=1/3(x-3)
y-2=1/3x-1
y=1/3x-1+2
y=1/3x+1      reduzida
r=1/3x-y+1=0   geral

b) A (4,5) B (0,1)
y-y0=m(x-x0)
m=yA-yB/xA-XB
m=5-1/4-0=4/4
m=1
y-y0=m(x-x0)
y-5=1(x-4)
y-5=x-4
y=x-4+5
y=x+1  reduzida
r=x-y+1=0  geral

c) A (2,-1) B (1,2)
y-y0=m(x-x0)
m=yA-yB/xA-XB
m=-1-2/2-1=-3/1
m=-3
y-y0=m(x-x0)
y-2=-3(x-1)
y-2=-3(x-1)
y=-3x+5  reduzida
r=3x+y-5=0 geral

d) A (3,5) B (2,-3)
y-y0=m(x-x0)
m=yA-yB/xA-XB
m=5-(-3)/3-2=8/1
m=8
y-y0=8(x-x0)
y-5=8(x-3)
y=8x-24+5
y=8x-19  reduzida
r=8x-y-19=0 geral