Question

Select the first step in the Construction of a perpendicular to a line from a point outside the line using a ruler and compass.

• A. Place the compass point at B and using the same distance, draw an arc to cut the previous arc at T.
• B. Placing the compass point at point K and using any convenient distance, draw arcs to cut the line MN at two points A and B.
• C. Place the compass point at A and taking a distance greater than half of AB, draw an arc on the lower side of line MN.
• D. Draw line MN and take any point K outside the line.

Answer 1

The correct option is D Draw line MN and take any point K outside the line.

Steps in the construction of a perpendicular to a line from a point outside the line using a ruler and compass are as follows:

1. Draw line MN and take any point K outside the line.
2. Placing the compass point at point K and using any convenient distance, draw arcs to cut the line MN at two points A and B.
3. Place the compass point at A and taking a distance greater than half of AB, draw an arc on the lower side of line MN.
4. Place the compass point at B and using the same distance, draw an arc to cut the previous arc at T.
5. Draw the line KT.

Line KT is perpendicular to line MN.
Hence the first step is:
Draw line MN and take any point K outside the line.