Slide It! Translating Shapes on a Grid

Imagine you place a book on a table. You slide it three spaces to the right — without flipping or spinning it. The book looks exactly the same; it just moved. Shapes on a grid can do the same thing! This kind of sliding move has a special name in maths.

A translation is a sliding move. You slide a shape to a new position on a grid without turning it or flipping it. Every corner of the shape moves the same distance in the same direction. We describe a translation in two parts: 1. How many squares right or left. 2. How many squares up or down. For example: '3 right and 2 up' means every corner of the shape moves 3 squares to the right AND 2 squares up. Important: after a translation, the shape looks identical to the original — same size, same direction. It has just slid to a new place. Worked Example: Look at triangle ABC on a grid. Its corners (we call them vertices) are at: A = (1, 1) B = (3, 1) C = (2, 3) We translate the triangle 4 right and 1 up. Add 4 to every x-number (the across number) and add 1 to every y-number (the up number): A → (1+4, 1+1) = (5, 2) B → (3+4, 1+1) = (7, 2) C → (2+4, 3+1) = (6, 4) Plot the new corners A′, B′, C′ and join them. The new triangle is exactly the same as the original — it has just slid across and up.