Question

Alice is designing a book shelf. The segment LQ represents the base of the book shelf. Alice wants to construct a line to represent a rack passing through R and parallel to side LQ. She uses a straightedge and compass to complete some steps of the construction, as shown below:

Which of these is likely to be her next step in constructing the rack parallel to LQ?


Answer Choices:


Place the compass at S and adjust its width to point P.


Without changing the width of the compass, fix the compass at P and draw an arc.


Without changing the width of the compass, place the compass at S or P and draw an arc similar to the one drawn.


Place the compass at N and adjust the width to a length that is greater than the length of segment NS.

Answer 1

The next step in constructing the rack parallel to LQ is:

Place the compass at S and adjust its width to point P.

Explanation:

The next step in constructing the rack parallel to LQ is place the compass at S (or P) and adjust its width to point P (or S).

Answer 2

Place the compass at S and adjust its width to point P.

Explanation:

Here are the remaining steps to complete the construction.

The next step for Alice is to place the compass at point S and adjust its width to point P.

Next step is, without changing the width, place the compass at point T, draw another arc and cut the previously drawn arc. Label the new point as U.

Now, using straightedge, join points R and U.

RU is the required line that passes through R and parallel to LQ.