Question

sara is constructing a line perpendicular to a given line through point a which is above the given line. sara places the compass at point a and sets the width of the compass to intersect the given line in two places. she labels the intersection points as point c and point d. what could be saras next step? changing the compass width to be less than half the length of the segment, place the compass at point c and draw an arc below the given line. changing the compass width to be less than half the length of the segment, place the compass at point a and draw a circle. without changing the compass width, place the compass at point c and draw an arc below the given line. use a straightedge to connect point a to point c.

Explanation:

When constructing a perpendicular line from a point above a given line, after getting two intersection - points (C and D) on the given line with the compass centered at the external point (A), the next step is to use the same compass width, place the compass at one of the intersection points (either C or D) and draw an arc below the given line. This is a standard step in the construction process to find the mid - point of the segment CD and eventually draw the perpendicular.

Answer:

C. Without changing the compass width, place the compass at point C and draw an arc below the given line.