Question

How many arcs will we need to make while constructing a perpendicular to a line at a point on the line using a compass.

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is D 4


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.
Hence, we need 4 arcs for the construction.