Flip (Reflection) — Definition, Formula & Examples
A flip is when you create a mirror image of a shape by reflecting it across a line. The shape stays the same size and shape but faces the opposite direction, just like looking in a mirror.
A flip, formally called a reflection, is a rigid transformation that maps every point of a figure to a corresponding point on the opposite side of a fixed line (the line of reflection), at an equal distance from that line.
How It Works
To flip a shape, you pick a line to flip it over — this is called the line of reflection. Each point in the shape moves straight across the line and lands the same distance away on the other side. The new shape is called the image. The image is the same size and shape as the original, but it faces the opposite way.
Worked Example
Problem: A triangle has a vertex at the point (1, 3). If you flip the triangle over the y-axis, where does that vertex end up?
Step 1: Find how far the point is from the line of reflection (the y-axis). The point (1, 3) is 1 unit to the right of the y-axis.
Step 2: Move the point the same distance to the other side of the y-axis. One unit to the left of the y-axis gives the new point.
Answer: The vertex lands at (-1, 3). It moved across the y-axis but stayed the same height.
Why It Matters
Understanding flips helps you recognize symmetry in everyday objects like butterflies, letters, and building designs. Reflections are one of the three basic moves (along with slides and turns) that you use throughout geometry to describe how shapes relate to each other.
Common Mistakes
Mistake: Confusing a flip with a slide (translation) because the shape looks the same.
Correction: In a flip, the shape faces the opposite direction (like a mirror image). In a slide, the shape faces the same direction — it just moves to a new spot.