Reflections are a type of transformation that creates a mirror image of a figure over a line, called the line of reflection. The reflected image is the same size and shape as the original, but it's flipped. Each point in the original figure has a corresponding point in the reflected image that is the same distance from the line of reflection.
Understanding reflections is crucial in geometry because it helps us analyze symmetry, understand spatial relationships, and solve geometric problems. We often reflect over the x-axis, y-axis, or the line $y=x$. Let's jump into practice problems!
Match each term with its correct definition:
| Term | Definition |
|---|---|
| 1. Reflection | A. The original figure before a transformation. |
| 2. Line of Reflection | B. A transformation that flips a figure over a line. |
| 3. Image | C. The figure after a transformation. |
| 4. Pre-image | D. A line that a figure is flipped over during a reflection. |
| 5. Transformation | E. A change in the position, size, or shape of a figure. |
Match the numbers to the letters.
Reflecting a point over the x-axis changes the sign of the ____ coordinate. Reflecting over the y-axis changes the sign of the ____ coordinate. The reflected image is always ____ to the original figure. A reflection is a type of ____.
Explain, in your own words, how you can determine the coordinates of a point after it has been reflected over the line $y = x$. Give an example.
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