Question

than the length of segment ac.

1. draw an arc which intersects line ab at two points. label these points d and e.
2. adjust the compass width to be greater than the length of segment dc and draw two arcs, centered at d and e, which intersect above line ab. label the point of intersection f.
3. draw a straight line through points f and c.
4. draw an arc which intersects line ab at two points. label these points r and s.
5. adjust the compass width to be greater than the length of segment cs and draw two arcs, centered at r and s, which intersect below line ab. label the point of intersection t.
6. draw a straight line through points t and c.

which student(s) successfully outlined a series of steps to complete the construction?
a. only elias
b. both elias and greyson
c. only greyson
d. neither elias nor greyson

Explanation:

Step1: Analyze Elias' steps

Elias' steps start with setting the compass width to be less than the length of segment \(AC\) (assumed first step). Then drawing an arc intersecting line \(AB\) at \(D\) and \(E\). Adjusting the compass width to be greater than \(DC\) and drawing arcs centered at \(D\) and \(E\) intersecting at \(F\). Finally, drawing a line through \(F\) and \(C\). This is a valid construction (likely of a perpendicular or some geometric relation).

Step2: Analyze Greyson's steps

Greyson's steps: First, assume a step (maybe related to a point). Then drawing an arc intersecting line \(AB\) at \(R\) and \(S\). Adjusting the compass width to be greater than \(CS\) and drawing arcs centered at \(R\) and \(S\) intersecting at \(T\). Then drawing a line through \(T\) and \(C\). But the initial arc - intersection (step 2) should be related to a point (like starting from a point \(C\) - if we assume the construction is of a perpendicular from \(C\) to \(AB\), Greyson's first arc - intersection (step 2) is not related to a proper starting point (should be related to the point from which we are constructing the perpendicular, say \(C\)).

Answer:

A. only Elias