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Image Coordinates

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 3 of 61.

With coordinates, a translation is plain arithmetic. Translating by ⟨a, b⟩ adds a to every x-coordinate and b to every y-coordinate: the point (x, y) goes to (x + a, y + b).

$Triangle DEF and its image after the translation by 5, negative 3$

Take the vector ⟨5, -3⟩. D(-2, 4) goes to (-2 + 5, 4 - 3), which is D'(3, 1). E(1, 4) goes to E'(6, 1), and F(-2, 6) to F'(3, 3). The x-coordinates change only by the first number and the y-coordinates only by the second.

Challenge

Triangle ABC is translated by ⟨-3, 5⟩. Write the coordinates of A', B' and C', 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 ImageImage CoordinatesThe 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