lesson
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What if you could push a toy car across a giant tiled floor without spinning it or flipping it over?
That straight, smooth slide is one of the most useful tricks in geometry!
The Sliding Map
A coordinate grid is a map with a flat sideways number line called the x-axis and an up-down number line called the y-axis crossing right at (0,0).
When a shape slides to a new spot on the grid without turning, spinning, or changing size, we call that move a translation.
📊Interactive diagram
How do mathematicians write down secret instructions to tell a shape exactly where to slide?
The Vector Code
We write slide instructions using a column vector, which stacks two numbers inside tall brackets like (xy).
The top number tells you how many steps to hop sideways (positive goes right, negative goes left), and the bottom number tells you how many steps to hop up or down (positive goes up, negative goes down).
📊Interactive diagram
To slide any corner point (x,y), you simply add the top vector number to its x-value and the bottom vector number to its y-value.
What happens when we slide a whole triangle across the map using this rule?