Sliding a Shape

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 1 of 61.

A translation slides a shape without turning or flipping it. Every point moves the same distance in the same direction, so the image is the same shape and the same size, and it faces the same way.

$Triangle PQR and its image PQR prime, slid 3 right and 2 up$

The move is written as a vector ⟨a, b⟩: a steps right and b steps up, and a negative number goes left or down. To read the vector off a picture, take one corner and its image and count. From P(1, 1) to P'(4, 3) is 3 right and 2 up, so the vector is ⟨3, 2⟩. Every other corner moves by the same ⟨3, 2⟩, which makes a quick check: Q(4, 1) lands on Q'(7, 3).

On the board, the move is Translate: type the shift right and the shift up, and press Apply. The board slides the shape. When it sits exactly on the dashed target, press Check.

Challenge

Triangle ABC and a dashed target are on the grid. Find the translation that slides ABC onto the target: enter the shift right and the shift up, press Apply, 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 ShapeDraw 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 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