When constructing perpendicular lines with a compass and straightedge, how should you start the construction?

open the compass and mark two points of intersection between arcs from the given line.

use a straightedge to find the length of the given line and then make an arc above it.

open the compass to the width of the original line to measure it.

use a straightedge to create two arcs above and below the original line.

The correct answer is:

Open the compass and mark two points of intersection between arcs from the given line.

Explanation:

We start out from a point on the line, swinging the compass around to intersect our line twice.

We then set the compass to a width wider than the one we began with.  We move the compass to one of the points of intersection with one of the arcs and our line, and construct an arc below the original arc.  Keeping the width of the compass the same, we move to the other point of intersection and draw another arc that intersects the one we just drew.  We then use a straightedge to draw a line through the point of intersection of these two smaller arcs and the original point on our line.

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step-by-step explanation: