# 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 shown

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?

Fix the compass at L and draw an arc above the line.

Without changing the width of the compass, place the compass at Q and draw an arc through L.

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

Without changing the width of the compass, place the compass at M and draw an arc.

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1. You say nothing about how you know that Q is "just above" L, or what that means.

I'd say (c) is the choice. You draw arcs centered at P and T, such that they intersect above and below L. Note that the arcs must have radius greater than LT=LP.

I get the feeling that Q is where the arcs intersect above L, so the intersection below L (at, say, S) means that QS is perpendicular to LM.

Incidentally, constructing LM does not really fit the bill to start with, since either P or T must be beyond the line segment. What it should say is that points L and M are marked on a line extending beyond LM.

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2. An architect plans to make a drawing of the room of a house. The segment LM represents the ceiling 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 shown below:

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3. UR MOM BROTHER FLAM GO FORM SU TART SAD STORY

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