When you study geometric transformations, there are four main ideas to know: translation, rotation, reflection, and enlargement. Let’s take a closer look at each one.

1. Translation

Translation is like sliding a shape across a flat surface without changing how it looks.

Think of it this way: imagine pushing a book along a table. The book stays the same, but it moves to a different spot.

In math terms, every point of the shape moves the same distance in the same direction.

For example, if you have a triangle with points at (A(1, 2)), (B(3, 4)), and (C(5, 6)) and you slide it 3 units to the right and 2 units up, the new points will be:

• (A'(4, 4))
• (B'(6, 6))
• (C'(8, 8))

2. Rotation

Rotation is when you turn a shape around a fixed spot, called the center of rotation.

You can turn it either clockwise or counterclockwise. We usually measure this in degrees.

For example, if you rotate the same triangle 90 degrees clockwise around the origin (which is the point (0,0)), the points would change like this:

• (A(1, 2)) becomes (A'(-2, 1))
• (B(3, 4)) becomes (B'(-4, 3))
• (C(5, 6)) becomes (C'(-6, 5))

3. Reflection

Reflection is like flipping a shape over a line to create a mirror image.

If you reflect a shape across the y-axis, for instance, every point (P(x, y)) will become (P'(-x, y)).

Using our triangle again, if we flip it over the y-axis, the points change like this:

• (A(1, 2)) becomes (A'(-1, 2))
• (B(3, 4)) becomes (B'(-3, 4))
• (C(5, 6)) becomes (C'(-5, 6))

4. Enlargement

Enlargement, also called dilation, changes the size of a shape but keeps its original shape the same.

This uses something called a scale factor, which tells us how much to make the shape bigger or smaller.

So, if we take our triangle and enlarge it with a scale factor of 2, the new points would be:

• (A'(2, 4))
• (B'(6, 8))
• (C'(10, 12))

Summary

In short, here’s what you need to remember:

• Translation is sliding.
• Rotation is turning.
• Reflection is flipping.
• Enlargement is resizing.

Knowing these concepts helps you build a strong foundation in geometry as you explore more shapes and ideas in math!