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Symmetry and transformations
Locate reflected points using equal distances from the mirror line.
Start with the picture
Choose the reference and rule, then examine properties such as lengths and angles that stay unchanged.
Check with another example
1. Reflect (2,1) in the y-axis. Which point results?
- (2,−1)
- (−2,−1)
- (−2,1)
My reason
2. What is always preserved by a plane reflection?
- Side lengths and angles
- The position of every point
- Always the same orientation
My reason
3. Reflect (3,−2) in the x-axis.
- (−3,−2)
- (3,2)
- (3,−2)
My reason
Explain in your own words
Name one similarity and one difference between reflection and translation.
Answers and reasons
1. (−2,1)
Yes. The point keeps the same distance from the y-axis on the other side.
2. Side lengths and angles
Reflection preserves distances, so it does not change the size of the shape.
3. (3,2)
Yes. The horizontal coordinate stays, while two units below becomes two above.
Both preserve lengths and angles. Reflection pairs points across a line; translation moves all points by the same vector.