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Question

Arrange the steps of construction of a perpendicular to a line at a point on the line using a compass in correct order:
(A).    Draw line MN and take point K anywhere on the line.
(B).    Place the compass point at A and, taking a convenient distance greater than half the length of AB, draw AN ARC on one side of the line. 
(C).    Place the compass point on point K. Draw TWO ARCS on either side of point K to cut the line MN at equal distances from K. Name the points of intersection A and B respectively. 
(D).    Draw a line passing through points K and T.
(E).     Place the compass point at B and using the same distance, draw ANOTHER ARC to intersect the first one at T. 
(F).      The line KT is perpendicular to line MN at K.
  1. A,B,C,D,E,F
  2. A,C,D,B,E,F
  3. A,C,B,E,D,F
  4. A,D,C,F,E,B


Solution

The correct option is C A,C,B,E,D,F
Steps of construction of a perpendicular to a line at a point on the line using a compass are as follows:
  • Draw line MN and take point K anywhere on the line.
  • Place the compass point on point K. Draw TWO ARCS on either side of point K to cut the line MN at equal distances from K. Name the points of intersection A and B respectively. 
  • Place the compass point at A and, taking a convenient distance greater than half the length of AB, draw AN ARC on one side of the line. 
  • Place the compass point at B and using the same distance, draw ANOTHER ARC to intersect the first one at T. 
  • Draw a line passing through points K and T. 
  • The line KT is perpendicular to line MN at K.
Line KT ⊥ line MN.
 

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