Indicate whether the following statement is true or false. If a figure can be translated, then it will tessellate.
a)True, all translations are tessellations.
b)False, not all translations are tessellations.
Is the answer a?
Try tessellating a circle.
The answer is B
To determine whether the given statement is true or false, we need to understand the concepts of translation and tessellation.
Translation: In geometry, a translation is a transformation that moves every point of a figure the same distance and in the same direction.
Tessellation: A tessellation is a pattern created by repeating a shape or a group of shapes without leaving any gaps or overlaps. In other words, a tessellation is a tiling of the plane.
To evaluate the statement, we need to consider whether every figure that can be translated can also tessellate.
The correct answer is option (b) False, not all translations are tessellations. While it is true that a translation does not introduce any gaps or overlaps in the shape being moved, it does not guarantee that the translated figure will be able to tessellate. Tessellations require specific shapes and arrangements to fill the entire plane without any gaps or overlaps. Some figures can be translated, but their shapes or arrangements may not allow them to form a tessellation.
To determine if a particular figure can tessellate, you would need to consider additional criteria such as the shape's angles, sides, and symmetry.