Slide (Translation) — Definition, Formula & Examples
A slide is the everyday name for a translation in geometry. It moves a shape to a new position by shifting every point the same distance in the same direction, without turning or flipping it.
A translation (slide) is a rigid transformation that maps each point of a figure to a new point by adding a fixed horizontal distance and a fixed vertical distance, preserving the figure's size, shape, and orientation.
How It Works
To slide a shape, pick how far to move it left or right and how far to move it up or down. Then move every point of the shape by exactly those amounts. The new shape, called the image, looks identical to the original — it is not rotated, flipped, or resized.
Worked Example
Problem: A triangle has vertices at A(1, 2), B(4, 2), and C(4, 5). Slide the triangle 3 units to the right and 2 units down. What are the new vertices?
Step 1: Add 3 to each x-coordinate (right) and subtract 2 from each y-coordinate (down).
Step 2: Find each new vertex.
A' = (1+3,\; 2-2) = (4,\; 0)$$ $$B' = (4+3,\; 2-2) = (7,\; 0)$$ $$C' = (4+3,\; 5-2) = (7,\; 3)
Answer: The new vertices after the slide are A'(4, 0), B'(7, 0), and C'(7, 3).
Why It Matters
Understanding slides helps you describe how objects move on a grid or map without changing shape. This idea comes up in art, tiling patterns, and later in coordinate geometry when you study transformations more formally.
Common Mistakes
Mistake: Moving different points by different amounts, which distorts the shape.
Correction: Every point must shift by the exact same distance in the exact same direction. That is what keeps the shape unchanged.