lesson
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When you slide a game piece across a board, it glides to a new spot without turning, flipping, or changing size.
In math, this sliding motion is called a translation, where every single corner of a shape moves the exact same distance in the exact same direction.
To give clear directions for a slide, we write a special math instruction called a column vector.
📊Interactive diagram
How do two stacked numbers tell us how to move in all four directions?
Reading a Column Vector
The top number tells you how many steps to move sideways along the x-axis—a positive number steps right, while a negative number steps left.
The bottom number tells you how many steps to move vertically along the y-axis—a positive number steps up, while a negative number steps down.
What happens when a shape slides all the way past zero into the negative grid zones?
Translating Across the Four Quadrants
A coordinate grid is split into four rooms called quadrants by the crossing axes, meeting at the center (0,0) called the origin.
Let's slide a triangle with corner A(1,2) using the column vector (−4−5).
Add the top number to the x-coordinate (1+(−4)=−3) and the bottom number to the y-coordinate (2+(−5)=−3), landing the new corner A′ at (−3,−3).