Question

find the area of ∆ formed by the line ax + by + c = 0 ​

Answer 1

ax+by+c=0

ax+by−c=0

ax−by+c=0

ax−by−c=0

These lines form a figure called rhombus

Area of rhombus is 12d1d2

Transform the equations

y=−abx−cb

y=−abx+cb

x=bay−ca

x=bay+ca

Find d1 by equations 1 and 2

Find d2 by equations 3 and 4

d1=2cb

d2=2ca

Area =12⋅2cb⋅2ca

AREA=2c2ab

Hope it helps!