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Perpendicular at a Point

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 48 of 61.

When the point P is on the line, make it a midpoint first. A circle about P crosses the line at two points, K and K', equally far from P. The perpendicular bisector of KK' then passes through P at right angles.

$A circle about P marks K and K prime; their perpendicular bisector passes through P$

That takes four tools: the circle about P, the two circles about K and K' (each through the other), and the line through their crossings. It is the perpendicular bisector construction from the last chapter, with K and K' made to order.

Challenge

P lies on the line AB. Construct the line through P perpendicular to AB, then press Check.

Try it yourself

$Construct it with a compass and straightedge$

Construct it with a compass and straightedge

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Transformations & Constructions

1Translations

Sliding a Shape Draw the Image Image Coordinates The Translation Rule Recap: Translations

4Combining Moves

One Move, Then Another Order Matters Two Mirrors Name the Move Recap: Combining Moves

7Drawing on Squared Paper

Lengths by Pythagoras Perpendicular Steps Squares by Area Right Triangles by Area Midpoints on the Grid Recap: Squared Paper

10Perpendiculars and Parallels

Perpendicular From a PointPerpendicular at a PointParallel Through a Point Tools You Have Earned Recap: Parallels