Question

1.8.7 check your understanding
an incomplete construction is shown.
what step of the construction is being illustrated?
adjust the width of the compass to point ( u ). the width of the compass is now equal to the length of ( overline{lu} ).
mark a point, ( v ), that will be one endpoint of the new line segment.
use a straightedge to draw a line segment from ( v ) to any point on the arc created.
without changing the width of the compass, place the compass point on ( v ). keeping the same compass width, draw an arc approximately where the other endpoint will be created.

Explanation:

To determine the construction step, we analyze each option:

• Option 1: Adjusting compass to \( \overline{LU} \) length is an earlier step (setting compass width), not the one shown (drawing arc from \( V \)).
• Option 2: Marking \( V \) is the initial step of defining the new segment’s endpoint, not the arc - drawing step here.
• Option 3: Drawing a segment from \( V \) to arc is the final step (connecting endpoints), not the current arc - drawing action.
• Option 4: After setting compass width to \( \overline{LU} \) and marking \( V \), placing compass on \( V \) and drawing an arc (to find the other endpoint) matches the illustration (arc drawn from \( V \)’s vicinity with compass).

Answer:

D. Without changing the width of the compass, place the compass point on \( V \). Keeping the same compass width, draw an arc approximately where the other endpoint will be created.