Question

which is an accurate description for step 2?
draw arcs, using a compass, above and below line segment xy with x as the center with a width of less than half of line segment xy
draw arcs, using a compass, above and below line segment xy with x as the center with a width of more than half of line segment xy
draw arcs, using a compass, above line segment xy with x as the center and below line segment xy with y as the center with a width of more than half of line segment xy
draw arcs, using a compass, above line segment xy with x as the center and below line segment xy with y as the center with a width equal to the half of the segment xy

Explanation:

Step1: Recall perpendicular bisector construction

To construct a perpendicular bisector of a line segment \(XY\), when using a compass, we need to draw arcs above and below the line segment \(XY\). The radius (width) of the arcs should be more than half of the length of \(XY\). If we use \(X\) as the center for arcs above and below \(XY\) with a radius more than half of \(XY\), then we can later use \(Y\) as the center (in other steps) to intersect these arcs and draw the perpendicular bisector.

Step2: Analyze each option

• Option 1: If the width (radius) is less than half of \(XY\), the arcs will not intersect to form the perpendicular bisector.
• Option 2: Drawing arcs above and below \(XY\) with \(X\) as the center and radius (width) more than half of \(XY\) is a valid step in constructing a perpendicular - related figure (like a perpendicular bisector or a right - angle at the mid - point).
• Option 3: We need arcs both above and below \(XY\) when starting with center \(X\) (for a more comprehensive construction, not just one - sided below with another center immediately in this step as per the general construction flow).
• Option 4: The width should be more than half (not equal to half) so that the arcs intersect.

Answer:

Draw arcs, using a compass, above and below line segment \(XY\) with \(X\) as the center with a width of more than half of line segment \(XY\)