Question

Adina is constructing a line perpendicular to YJ←→YJ↔ . She has already constructed two arcs as shown.


She moves her compass point to Y to construct an arc above the line.

What must be true about the width of Adina’s compass opening before she draws the arc?

It must be the same as it was when constructing the first two arcs.

It must be wider than it was when constructing the first two arcs.

It must be narrower than it was when constructing the first two arcs.

Answer 1

When drawing the arcs above and below the line YJ, the compass must be set wider than the length of YC, otherwise the arcs produce will pass through the point C (it won't give a line that is perpendicular to YJ through C)

Answer: It must be wider than it was when constructing the first two arcs.

Answer 2

The correct answer is:

It must be wider than it was when constructing the first two arcs.        

Explanation:

In order to construct the first two arcs, Adina had her compass on point C.  If we have the compass set to a smaller width than YC or CJ, we will not be able to draw an arc to intersect it.

For instance, if we set our compass on point Y at a width smaller than that of YC and create an arc, then move to point J to try to intersect it, the arc will not intersect.