lesson
Updated 6 days ago · 2 views
When you pinch-to-zoom on a photo on your phone, the picture grows larger, but faces and buildings never get warped or squished.
In geometry, this resizing transformation is called an enlargement (sometimes called a dilation).
An enlargement is a transformation that changes the size of a figure while preserving its exact shape.
📊Interactive diagram
What does it mean mathematically for a figure to keep its shape?
What Stays the Same vs. What Changes
During an enlargement, every internal angle stays exactly the same, which ensures the figure never bends or warps.
Every side length changes by the exact same multiplier, producing two figures that are similar (identical in shape, differing only in size).
Around 300 BCE, the Greek mathematician Euclid established these principles of geometric similarity in Book VI of his Elements to explain proportional figures.
📊Interactive diagram
What happens if you stretch a shape horizontally without stretching it vertically?
Enlargement vs. Distortion
If you multiply the width of a rectangle by 3 but keep its height the same, the proportions change and the rectangle becomes long and skinny.