what graph demonstrates a transformation that preserves both distance and angle measure
A rigid transformation, such as a translation, rotation or reflection, preserves both distance and angle measure. These transformations do not alter the shape of the object, only its position or orientation in space. Hence, any graph or figure before and after a rigid transformation will have congruent corresponding sides and angles.
A graph that demonstrates a transformation preserving both distance and angle measures is called an isometry. Isometries are transformations that maintain the same shape, size, and orientation of a figure. There are three types of isometries: reflections, translations, and rotations.
1. Reflection: A reflection is a transformation that flips a figure across a line called the axis of reflection. The distance between any two points on the figure and their corresponding points after reflection remains the same. Additionally, the angle measure between any two intersecting lines or line segments is preserved.
2. Translation: A translation is a transformation that slides a figure along a straight line without changing its shape, size, or orientation. The distance between any two points on the figure and their corresponding points after translation remains the same. Similarly, the angle measure between any two intersecting lines or line segments is preserved.
3. Rotation: A rotation is a transformation that turns a figure around a fixed point called the center of rotation. The distance between any two points on the figure and their corresponding points after rotation remains the same. Likewise, the angle measure between any two intersecting lines or line segments is preserved.
In summary, any graph that demonstrates a reflection, translation, or rotation is an example of a transformation that preserves both distance and angle measure.
The graph that demonstrates a transformation preserving both distance and angle measure is called an isometry. An isometry is a transformation that preserves the shape and size of an object. It includes translations, rotations, and reflections.
To determine if a translation preserves distance and angle measure, you can follow these steps:
1. Start with an original figure or shape.
2. Apply a translation by moving the figure along a straight path, without changing the orientation or size of the figure.
3. Measure the lengths of the sides of the original figure and the translated figure using a ruler.
4. Compare the measurements of the corresponding sides. If they are equal, it means that the translation preserved the distance.
5. Additionally, measure the angles of the original figure and the translated figure using a protractor.
6. Compare the measurements of the corresponding angles. If they are equal, it means that the translation preserved the angle measure.
If a transformation satisfies both the preservation of distance and angle measure, it can be represented graphically as an isometry. This means that all corresponding sides and angles of the original figure and the transformed figure are congruent.