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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:yx+1=0(i)   Both points lie on the same side of the line(p)   755 units(II)   L2:6y+x11=0(ii)   Both points lie on the opposite side of the line(Q)   22 units(III)   L3:y2x+2=0(iii)   Both points lie on the line(R)   253737 units(IV)   L4:3y+x13=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?


  1. (II) (i) (Q)
  2. (I) (iv) (Q)
  3. (IV) (i) (S)
  4. (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+ca2+b2
 Perpendiculardistance from LinePoint A(1,4)Point B(4,3)Sum of distanceL1:yx+1=022022L2:6y+x11=014371137252737L3:y2x+2=04535755L4:3y+x13=0000
Now, Match the options

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