Rigid motions are transformations that preserve the size and shape of a geometric figure. In other words, if you apply a rigid motion to a figure, the resulting figure will be congruent to the original figure. There are four main types of rigid motions:...
- Translation: Moving a figure to a new location without changing its orientation.
- Rotation: Turning a figure around a fixed point.
- Reflection: Flipping a figure over a line.
- Glide reflection: A combination of a reflection and a translation.
What is dilation?
Dilation is a transformation that changes the size of a figure but not its shape. It's like zooming in or out on a picture. A dilation is defined by a scale factor, which determines how much the figure is enlarged or shrunk. A scale factor greater than 1 results in an enlargement, while a scale factor less than 1 results in a reduction.
Why dilation is not a rigid motion
Dilation is not a rigid motion because it does not preserve the size of the figure. If you dilate a figure, the resulting figure will be similar to the original figure (same shape, different size), but not congruent. This means that the corresponding sides of the two figures will be proportional, but not equal in length.
Example of dilation
Imagine you have a triangle with sides of length 3, 4, and 5. If you dilate this triangle by a factor of 2, the new triangle will have sides of length 6, 8, and 10. The new triangle is similar to the original triangle because the corresponding angles are equal, but it's not congruent because the sides are not the same length.
Answer to the question
Therefore, the answer to the question "Which transformation is not a rigid motion?" is **B. Dilate by a factor of 2.**
Summary
Rigid motions preserve both the size and shape of a figure, while dilations only preserve the shape. A dilation will change the size of a figure but not its shape. Therefore, dilation is not a rigid motion.