  Question

# Column – 1 represents equation of straight lines Column – 2 represents position of points A ≡ (1, 4) and B(4, 3) w.r.t. equation of line in Column - 1 Column – 3 represents the sum of length of perpendiculars from points A and B to the lines in Column-1 Column 1Column 2Column 3(I)   L1:y−x+1=0(i)   Both points lie on the same side of the line(p)   7√55 units(II)   L2:6y+x−11=0(ii)   Both points lie on the opposite side of the line(Q)   2√2 units(III)   L3:y−2x+2=0(iii)   Both points lie on the line(R)   25√3737 units(IV)   L4:3y+x−13=0(iv)   One point (out of A, B) lie on the line(S)   0 units Which of the following options is the only CORRECT combination? (II) (i) (Q)(I) (iv) (Q)(IV) (i) (S)(I) (ii) (P)

Solution

## The correct option is B (I) (iv) (Q)Using S1 and S2, we can say that L1 passes through one of the points L2 have both the points on the same side L3 have both the points on the opposite side L4 have both the points on the line For perpendicular distance, use formula ∣∣∣ax1+by1+c√a2+b2∣∣∣  Perpendiculardistance from LinePoint A(1,4)Point B(4,3)Sum of distanceL1:y−x+1=02√202√2L2:6y+x−11=014√3711√3725√2737L3:y−2x+2=04√53√57√55L4:3y+x−13=0000 Now, Match the options  Suggest corrections   