which transformation is the image not congruent
line reflection
translation
rotation dilation
To determine which transformation does not result in a congruent image, we need to review what congruence means for each type of transformation:
1. Line Reflection: A line reflection is a transformation that flips an image across a line, known as the line of reflection. It preserves both the size and shape of the original shape, resulting in a congruent image.
2. Translation: Translation involves moving an object from one location to another without any change in size or shape. Since translation preserves both the size and shape of the object, it produces a congruent image.
3. Rotation: A rotation is a transformation that turns an object around a fixed point called the center of rotation. Depending on the angle of rotation, the size and shape of the object may or may not be preserved. If the angle of rotation is a multiple of 90 degrees (e.g., 90°, 180°, 270°), the resulting image will be congruent. However, if the angle of rotation is any other value, the shape and size of the object will change, resulting in a non-congruent image.
4. Dilation: Dilation involves changing the size of an object while keeping its shape intact. If the scale factor of dilation is equal to 1, the image will be congruent to the original. However, if the scale factor is different from 1, the image will change in size and therefore will not be congruent.
From the above explanations, we can see that the transformation that does not guarantee congruence is a rotation. If the angle of rotation is any value other than a multiple of 90 degrees, the resulting image will not be congruent to the original.