Point of intersection of ℓ1:3y−2x=3 ℓ2:x−y+1=0 is P≡(0,1) Which lies on ℓ3:αx−βy+17=0, ⇒β=−17 Consider a random point Q≡(−1,0) on ℓ2:x−y+1=0, image of Q about ℓ2:x−y+1=0, is Q′≡(
−17
13
,
6
13
) which is calculated by formulae
x−(−1)
2
=
y−0
−3
=2(
−2+3
13
) Now, Q′ lies in ℓ3:αx+βy+17=0 ⇒α=7 Now, α2+β2−α−β=348