Translation and reflection — on x and y axis

In geometry, a transformation is a way of changing the position, size, or orientation of a shape. Think of it like moving a sticker on a page — the sticker itself doesn't change, but where it sits (or how it faces) does.

In this subtopic, we focus on two specific types of transformations:

• Translation — sliding a shape from one place to another
• Reflection — flipping a shape over a line (like looking in a mirror)

Both of these are called rigid transformations (or isometries), which means the shape stays exactly the same size and shape — nothing stretches or shrinks.

Before we translate or reflect shapes, let's make sure we're comfortable with the coordinate plane (also called the Cartesian plane).

• The x-axis is the horizontal line (left–right)
• The y-axis is the vertical line (up–down)
• They cross at the origin, which is the point $(0,0)$
• Every point is written as an ordered pair $(x,y)$

The plane is divided into four quadrants:

• Quadrant I: $x>0$, $y>0$ (top-right)
• Quadrant II: $x<0$, $y>0$ (top-left)
• Quadrant III: $x<0$, $y<0$ (bottom-left)
• Quadrant IV: $x>0$, $y<0$ (bottom-right)