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The Midpoint

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 42 of 60.

A construction can find the exact middle of a segment without measuring it. The perpendicular bisector crosses the segment at its midpoint, so the midpoint costs one extra Point tap, which is free.

$The perpendicular bisector of KL meets it at its midpoint M$

For KL: build the perpendicular bisector with two circles and a line, then mark M where it crosses KL. M is equally far from K and from L because every point on the bisector is, and it lies on KL, so it is exactly halfway.

Challenge

Construct the midpoint of AB, then press Check.

Try it yourself

$Construct it with a compass and straightedge$

Construct it with a compass and straightedge

All lessons in Transformations & Constructions

1Translations

Sliding a Shape Draw the Image 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 Point Perpendicular at a Point Parallel Through a Point Tools You Have Earned Recap: Parallels

3Rotations

Turning About a Point The Half Turn Quarter-Turn Rules A Center Off the Origin Recap: Rotations

6Symmetry

Lines of Symmetry Rotational Symmetry Regular Polygons Symmetry Is a Move Recap: Symmetry

9Bisectors

The Perpendicular BisectorThe MidpointBisecting an Angle Half of 60°Recap: Bisectors

12Final Challenges

Final: Footprints Final: Two Moves, One Rule Final: Mirror on the Grid Final: The Fair Well Final: The Tangent Road