Lengths by Pythagoras

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 31 of 61.

On squared paper every slanted segment between two grid nodes is the long side of a right triangle whose legs run along the grid lines. So its length comes from the Pythagorean theorem: going a across and b up makes a segment of length √(a² + b²).

$A segment 2 across and 1 up, the long side of a right triangle with legs 2 and 1$

The segment AC goes 2 across and 1 up, so AC = √(2^2 + 1^2) = √(5). No square on the grid has a side of √5 along a grid line, yet a slanted segment gets it exactly. To draw a given length √n, look for two whole numbers whose squares add up to n.

On the board, tap a node to start a segment and another node to end it. The readout shows its length.

Challenge

On the squared paper, draw a segment of length √13 from one grid node to another, then press Check.

Test yourself

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

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 PythagorasPerpendicular 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