Question

An architect plans to make a drawing of the room of a house. The segment LM represents the floor of the room. He wants to construct a line passing through Q and perpendicular to side LM to represent a wall of the room. He uses a straightedge and compass to complete some steps of the construction, as described:

A line segment LM is drawn.
Two arcs equidistant from L on line LM are drawn at points P and T.
A point Q is just above L.
A compass is fixed at point Q and is shown making an arc at T.

Which of these is likely to be his next step in constructing the perpendicular line?

A.) Fix the compass at L and draw an arc above the line.
B.) Without changing the width of the compass, place the compass at Q and draw an arc through L.
C.) Fix the compass at points P and T and draw arcs which intersect below the line.
D.) Without changing the width of the compass, place the compass at M and draw an arc.

Answer 1

Fix the compass at points P and T, and draw arcs which intersect below the line.

Explanation:

Answer 2

Fixing the compass at points P and T and drawing arcs which intersect below the line is likely to be his next step in constructing the perpendicular line.

In elementary geometry, the property of being perpendicular(perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects. A line is said to be perpendicular to another line if the two lines intersect at a right angle.

The correct answer between all the choices given is the third choice or letter C. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.