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Midpoints on the Grid

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 35 of 61.

The midpoint of a segment is halfway along it. On squared paper, go half the steps across and half the steps up from one end. In coordinates, average the two ends: the midpoint of (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂)/2, (y₁ + y₂)/2).

$The midpoint M of the segment PQ$

PQ goes 4 across and 2 up. Half of that is 2 across and 1 up, so the midpoint M is at (3, 2). The averages say the same: (1 + 5)/2 = 3 and (1 + 3)/2 = 2.

On the board, the Point tool places a point on a grid node.

Challenge

Place a point at the midpoint of AB, then press Check.

Try it yourself

$Draw it on squared paper$

Draw it on squared paper

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 AreaMidpoints on the GridRecap: Squared Paper

10Perpendiculars and Parallels

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