A____ is the same distance from each point of a figure and its image.
translation vector
center of rotation
rigid transformation
line of reflection
rigid transformation
A line of reflection is the same distance from each point of a figure and its image.
The correct answer is a "line of reflection."
To understand why, we need to have a basic understanding of transformations in geometry. A transformation is a way to move or change the position of a figure in space. The four types of transformations commonly studied in geometry are translations, rotations, reflections, and dilations.
In this question, the figure and its image are being compared. The figure refers to the original shape, and the image refers to the shape after a transformation has been applied.
A line of reflection is a transformation that flips a figure over a line. It is a type of reflection, where every point on the original figure is reflected across the line to create the image. Importantly, the line of reflection is equidistant from each point on the figure and its image. This means that the distance from any point on the figure to the line of reflection is the same as the distance from the corresponding point on the image to the line of reflection.
On the other hand, a translation vector refers to the direction and distance by which a figure is moved to create its image. It does not necessarily result in equal distances between each point of the figure and its image.
The center of rotation is the point about which a figure is rotated. While a rotation can preserve the distance between certain points, it does not guarantee that every point in the figure and its image will have equal distances.
A rigid transformation is a general term for a transformation that preserves shape and size. It includes translations, rotations, and reflections. While a line of reflection is a specific type of rigid transformation that preserves distances, not all rigid transformations have this property.
Therefore, the line of reflection is the correct answer as it is the transformation that results in equal distances between each point of the figure and its image.