Hey there! Ready to explore how shapes move without changing their size or shape? Let's dive into the world of geometric translations!
A translation is a slide. It moves every point of a shape the exact same distance in the exact same direction, like a chess piece sliding across the board.
When we translate a shape, it keeps its original size, shape, and orientation. The original shape is called the 'pre-image', and the new shape is called the 'image'.
We describe a translation using a rule like (x, y) → (x + a, y + b). This tells us exactly how many units to slide right or left (x), and up or down (y).
✏️ Worked example
Translate the point A(2, 3) using the translation rule: (x, y) → (x + 3, y - 4). Find the coordinates of the new image point A'.
Identify the original coordinates of point A, which are x = 2 and y = 3.
Apply the rule for the x-coordinate: add 3 to the original x-value. So, 2 + 3 = 5.
Apply the rule for the y-coordinate: subtract 4 from the original y-value. So, 3 - 4 = -1.
Combine the new coordinates to write the final image point: A'(5, -1).
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