Question

select the correct answer. what is the first step in the construction of a line perpendicular to $overleftrightarrow{ab}$ and passing through an external point $m$? assume that the construction uses only a compass and a straightedge. a. place the compass needle on $m$ and, keeping the compass width the same, draw two arcs that intersect $overleftrightarrow{ab}$. b. place the compass needle at any point on $overleftrightarrow{ab}$, and set the compass width to $m$. c. draw a line from point $m$ passing through $overleftrightarrow{ab}$, and mark the point of intersection. d. place the compass needle at any two points on $overleftrightarrow{ab}$, and draw two arcs through $m$.

Explanation:

To construct a line perpendicular to a given line $\overleftrightarrow{AB}$ from an external point $M$ using only a compass and straight - edge, the first step is to place the compass needle on $M$ and, keeping the compass width the same, draw two arcs that intersect $\overleftrightarrow{AB}$. This allows us to create equal - length segments on $\overleftrightarrow{AB}$ which are used in subsequent steps to find the perpendicular.

Answer:

A. Place the compass needle on $M$ and, keeping the compass width the same, draw two arcs that intersect $\overleftrightarrow{AB}$