Question

What is the first step in the construction of a line perpendicular to a ¢ b Ÿ· and passing through an external point m? Assume that the construction uses only a compass and a straightedge.

1) Place the compass needle on m and, keeping the compass width the same, draw two arcs that intersect a ¢ b Ÿ· .
2) Place the compass needle at any point on a ¢ b Ÿ· , and set the compass width to m.
3) Draw a line from point m passing through a ¢ b Ÿ· , and mark the point of intersection.
4) Place the compass needle at any two points on a ¢ b Ÿ· , and draw two arcs through m.

Answer 1

The first step in constructing a perpendicular line is to draw two arcs that intersect the given line at the external point.

Step-by-step explanation:

To construct a line perpendicular to a line‾AB and passing through an external point

M using only a compass and a straightedge, the correct first step is 2) Place the compass needle at any point on AB, and set the compass width to M.

Here's a step-by-step explanation:

Place the compass needle at any point on ‾AB: This step involves selecting an arbitrary point on the given line. Set the compass width to M: Adjust the compass width to the distance between the point where the compass needle is placed and the external point M.

Draw arcs with the compass: Using the compass, draw two arcs from the selected point on ‾AB, intersecting the line on both sides.

Label the intersection points: Label the points where the arcs intersect the line asP and Q.Draw a straight line through M and the intersection points: Use a straightedge to draw a line through M and the points P and Q. This line will be perpendicular to AB

Option 2 correctly follows the standard construction method for creating a perpendicular line using a compass and a straightedge. The other options do not adhere to the proper construction process.