Order Matters

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 17 of 61.

The same two moves done in the other order can land in a different place. A combination of moves is read in order, and swapping the order is a different move.

Take P(2, 1). Translate by ⟨0, 3⟩ and then reflect in the x-axis: the slide gives (2, 4) and the mirror gives (2, -4). Now reflect first and slide second: the mirror gives (2, -1) and the slide gives (2, 2). Same two moves, two different images.

$One point, two orders of the same moves, two different images$

Some pairs do give the same result either way, such as two translations. Unless you know that, keep to the order the task gives.

Challenge

Triangle ABC is translated by ⟨2, 0⟩ and then rotated 90° counterclockwise about the origin, in that order. 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 Image Image Coordinates The Translation Rule Recap: Translations

4Combining Moves

One Move, Then AnotherOrder MattersTwo 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