Question

10.2 what’s the same? draw each rigid transformation in a different color. 1. translate figure s along the line segment v in the direction shown by the arrow. color: 2. reflect figure s across line y. color: ______ 3. reflect figure s across line m. color: ____ 4. translate figure s along the directed line segment w in the direction shown by the arrow. reflect this image across line y. color: ______ 5. how are the images the same? how are they different?

Explanation:

Step1: Understand translation

Translation moves a figure without rotation or reflection. For the first translation of Figure S along line - segment v, we move each point of Figure S the length and in the direction of v.

Step2: Understand reflection across line y

To reflect Figure S across line y, we find the perpendicular distance of each point of Figure S from line y and then place the new point at the same distance on the other side of line y.

Step3: Understand reflection across line m

Similar to the reflection across line y, for reflection across line m, we find the perpendicular distance of each point of Figure S from line m and place the new point at the same distance on the other side of line m.

Step4: Combined transformation

First, translate Figure S along line - segment w. Then, reflect the translated figure across line y. For the translation along w, we move each point of Figure S the length and in the direction of w. For the reflection across line y, we follow the same perpendicular - distance rule as before.

Step5: Analyze similarities and differences

The images are the same in that they all have the same shape and size because rigid transformations (translations and reflections) preserve shape and size (congruence). They are different in their position and orientation in the coordinate plane. Translations move the figure to a different location, and reflections flip the figure across a line, changing its orientation.

Answer:

1. (Draw the translated Figure S along v in a chosen color)
2. (Draw the reflected Figure S across line y in a different color)
3. (Draw the reflected Figure S across line m in a different color)
4. (Draw the figure after translation along w and then reflection across line y in a different color)
5. Same: Shape and size are preserved. Different: Position and orientation in the plane are different.