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The Translation Rule

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 4 of 61.

A rule says where every point goes. The rule (x, y) → (x + 2, y - 3) is the translation by ⟨2, -3⟩: it adds 2 to x and takes 3 from y, for any point at all.

$Triangle GHJ and its image, moved 5 left and 2 up$

To find a rule from a picture, read the vector from one corner to its image, then put it in the rule. G(2, 1) goes to G'(-3, 3): that is 5 left and 2 up, the vector ⟨-5, 2⟩. So the rule is (x, y) → (x - 5, y + 2). Test it on H(5, 1): it gives (0, 3), which is H'.

On the board, type the rule in the form (x - 5, y + 2), then press Check. The board tries your rule on every corner.

Challenge

Triangle ABC and its image are drawn on the grid. Write the rule that takes ABC onto its image, in the form (x + a, y + b), then press Check.

Try it yourself

$Move the shape onto its target$

Move the shape onto its target

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 CoordinatesThe Translation RuleRecap: 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