Question

standard: g.gsr.4.3-dok1
which of these is the first step in constructing a line perpendicular to \\( \overline { l m } \\) through point \\( b \\)?
construct the midpoint of \\( \overline { l m } \\).
use a ruler to draw a line through point \\( b \\) that is perpendicular to \\( \overline { l m } \\).
place the compass on \\( l \\) and draw an arc that is more than halfway across \\( \overline { l m } \\)
place the compass on \\( b \\) and draw a single arc that intersects \\( \overline { l m } \\) twice.

Explanation:

Step1: Analyze each option

• Option 1: Constructing the midpoint of \( \overline{LM} \) is not relevant to constructing a perpendicular through point \( B \).
• Option 2: Using a ruler to directly draw a perpendicular is not a valid geometric construction step (should use compass - and - straight - edge construction).
• Option 3: Placing the compass on \( L \) is not the first step for constructing a perpendicular through \( B \).
• Option 4: When constructing a perpendicular line to \( \overline{LM} \) through an external point \( B \), the first step is to place the compass on \( B \) and draw a single arc that intersects \( \overline{LM} \) twice. This is the basis for creating congruent segments to start the perpendicular construction.

Answer:

Place the compass on \( B \) and draw a single arc that intersects \( \overline{LM} \) twice.