Question

select all the statements that describe the steps to copy (overline{xy}).
diagram of segment (xy) with (x) and (y)
a. use a ruler to draw line (ell) and label point (m).
b. use a straightedge to draw line (ell) and label point (m).
c. place a compass point at (x) and open the compass to length (xy).
d. using the same setting, place the compass at point (m), draw an arc through line (ell), and mark point (n) as the intersection.
e. with a setting greater than (\frac{1}{2}xy), place the compass point at (x). draw arcs above and below (overline{xy}).

Explanation:

To copy a segment \(\overline{XY}\), the standard steps are:

1. Draw a line and label a point: We use a straightedge (not a ruler for just drawing the line; a straightedge is for drawing straight lines) to draw line \(\ell\) and label a point \(M\) on it (this is the starting point of the copied segment). So option B is correct, A is incorrect (ruler is for measuring, straightedge for drawing lines).
2. Set the compass to the length of \(\overline{XY}\): Place the compass point at \(X\) and open it to the length \(XY\) (so that the compass can transfer this length). This is option C.
3. Transfer the length: Using the same compass setting (which is the length \(XY\)), place the compass at point \(M\) and draw an arc that intersects line \(\ell\). The intersection point \(N\) will be such that \(MN = XY\), so \(\overline{MN}\) is a copy of \(\overline{XY}\). This is option D.

Option E describes steps for constructing a perpendicular bisector (since we use a setting greater than \(\frac{1}{2}XY\) and draw arcs above and below), which is not part of copying a segment.

Answer:

B. Use a straightedge to draw line \(\boldsymbol{\ell}\) and label point \(M\).
C. Place a compass point at \(X\) and open the compass to length \(XY\).
D. Using the same setting, place the compass at point \(M\), draw an arc through line \(\boldsymbol{\ell}\), and mark point \(N\) as the intersection.