Perpendicular through a point worksheets

Drop a perpendicular from a point to a line — the same four steps whether the point sits on the line or above it, which is the thing worth noticing.

Perpendicular through a point
Perpendicular through a point worksheet — P on the line and 10–26mm off it, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Swing an arc from P that crosses the line twice, then equal arcs from those two crossings; the line from P through where they meet is perpendicular to the original. It is the perpendicular-bisector construction wearing different clothes: the two crossings on the line are equidistant from P, so P is already on their bisector, and the construction just finds a second point on it.

Why this sheet works

Seeing that one construction do both jobs — a point on the line and a point off it — is the point of putting them on one sheet. A child who treats them as two separate recipes has learned twice as much as they needed to; a child who notices the arcs are the same has learned why it works.