![]() ![]() ![]() Although your quarter has had the adventure of a lifetime, the net result is not very impressive it started its day on the dresser and ended its day on the dresser. You go to school, hang out at the mall, flip it to see who gets the ball first in a game of touch football, return home exhausted and put it back on your dresser. In the morning you pick it up and put it in your pocket. It doesn't matter what happens in between.Ĭonsider the following example: suppose you have a quarter sitting on your dresser. In studying isometries, the only things that are important are the starting and ending positions. In this case P = P´ and P is called a fixed point of the isometry. It is possible for a point to end up where it started. Under an isometry, the image of a point is its final position.Ī fixed point of an isometry is a point that is its own image under the isometry.Īn isometry in the plane moves each point from its starting position P to an ending position P´, called the image of P. These will be discussed in more detail as the section progresses.Īn isometry is a transformation that preserves the relative distance between points. The four types of rigid motion (translation, reflection, rotation, and glide reflection) are called the basic rigid motions in the plane. These transformations are also known as rigid motion. There are many ways to move two-dimensional figures around a plane, but there are only four types of isometries possible: translation, reflection, rotation, and glide reflection. Whenever you transform a geometric figure so that the relative distance between any two points has not changed, that transformation is called an isometry. But the location of the ants relative to each other has not. The location of the ants will change relative to the plane (because they are on the triangle and the triangle has moved). Imagine two ants sitting on a triangle while you move it from one location to another. The word isometry is used to describe the process of moving a geometric object from one place to another without changing its size or shape. ![]()
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