Reflections are really cool changes in geometry. They flip shapes over a line, which changes where their points are and how they face. Let’s take a closer look!

How Reflections Change Coordinates:

1. Reflecting Over the x-axis:

   • When we flip a point $(x, y)$ over the x-axis, it changes to $(x, -y)$.
   • Example: The point $(3, 4)$ becomes $(3, -4)$.

2. Reflecting Over the y-axis:

   • If we reflect a point $(x, y)$ over the y-axis, it turns into $(-x, y)$.
   • Example: The point $(3, 4)$ flips to $(-3, 4)$.

3. Reflecting Over the line $y = x$:

   • When reflecting over this line, we switch the coordinates. So, $(x, y)$ changes to $(y, x)$.
   • Example: The point $(3, 4)$ becomes $(4, 3)$.

How It Affects the Shape:

• The shape keeps its size and form but switches how it faces.

  • For example, if a triangle is pointing up, flipping it over the x-axis will make it point down.

• This also changes the order of points when you draw the shape's outline.

See It Like This:

Think about how a mirror works. When you flip a picture in a mirror, the points change, and the overall look of the shape is different too!