Problem

Construct point \(Q\) on ray \(PX\) so \(PQ=AB\) using a compass and straightedge. State the compass opening, center, ray-marking action, and resulting equality.

Big Picture

What this problem is really about

A compass copies a length by carrying the distance itself, so no numerical measurement or rounding is needed. We’ll separate the source segment from the target ray, preserve one compass opening between them, and use the radius property at the new center to certify that the constructed segment is exact.

Answer choices

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Preview only

opening = compass width AB; center = P; ray action = name Q before intersecting the ray; result = PQ=AB

opening = compass width AB; center = P; ray action = mark intersection Q on ray PX without changing width; result = PQ=AB

opening = compass width AB; center = X; ray action = mark arc point Q; result = PQ=AB

opening = ruler measurement of AB; center = P; ray action = mark numerical distance Q; result = PQ approximately AB

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Construct point \(Q\) on ray \(PX\) so \(PQ=AB\) using a compass and straightedge. State the compass opening, center, ray-marking action, and resulting equality.

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