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Which transformation does not always result in an image that is congruent to the original figure?
A dilation (or scaling) is a transformation that does not always result in an image that is congruent to the original figure. While translations, rotations, and reflections always produce congruent figures, dilations change the size of the figure, which means the image may be similar to, but not congruent with, the original figure.
Does an isosceles trapezium have any perpendicular lines?
In its normal orientation the parallel sides of a trapezium are horizontal. In that case it will have no perpendicular lines. But turn the figure through 90 degrees and it has two!In its normal orientation the parallel sides of a trapezium are horizontal. In that case it will have no perpendicular lines. But turn the figure through 90 degrees and it has two!In its normal orientation the parallel sides of a trapezium are horizontal. In that case it will have no perpendicular lines. But turn the figure through 90 degrees and it has two!In its normal orientation the parallel sides of a trapezium are horizontal. In that case it will have no perpendicular lines. But turn the figure through 90 degrees and it has two!
Why does a reflection not preserve orientation of a figure on the plane?
Because a reflection reverses the direction of the component of the wave vector of the light hitting the reflecting surface which is orthogonal to the surface. The component parallel to the surface will not change. This means the light going towards a mirror, will go away from the mirror after reflection. But if it went from the left to the right, it will continue to go from the left to the right. Same with up and down. In three dimensions this is the same as changing the handedness of the image.
What happens to the x and y coordinates when rotating a figure counterclockwise?
A rotation is a transformations when a figure is turned around a point called the point of rotation. The image has the same lengths and angle measures, and differs only in position. Rotations that are counterclockwise are rotations of positive angles. All rotations are assumed to be about the origin. R90 deg (x, y) = (-y, x) R180 deg (x, y) = (-x, -y) R270 deg (x, y) = (y, -x) R360 deg (x, y) = (x, y)
The change in position from the shaded figure to the unshaded figure is best described as a?
Missing diagram.
Identify the transformation(s) where the image has the same orientation as the preimage.?
Transformations that preserve the orientation of the image relative to the preimage include translations, rotations, and dilations. These transformations maintain the order of points and the overall direction of the figure. In contrast, reflections and certain types of glide reflections change the orientation, resulting in a mirror image. Therefore, only translations, rotations, and dilations keep the same orientation as the original figure.
What type of transformation changes the orientation of a figure?
A transformation that changes the orientation of a figure is called a reflection. In a reflection, the figure is flipped over a line, known as the line of reflection, resulting in a mirror image that has a reversed orientation. Other transformations, such as rotations and translations, do not change the orientation of the figure.
Can rigid motions change the size of a figure?
No, rigid motions cannot change the size of a figure. Rigid motions, such as translations, rotations, and reflections, preserve the shape and size of geometric figures, meaning that the distances between points and the angles remain unchanged. Therefore, the figure retains its original dimensions throughout the transformation.
Why does a translation not preserve orientation of a figure?
A translation does not preserve the orientation of a figure because it simply shifts the entire figure in a specific direction without changing its shape or size. While the relative positions of the points within the figure remain consistent, the overall orientation can be perceived differently, especially in relation to other figures or coordinate axes. For example, if a triangle is translated, its vertices move to new locations, potentially altering its alignment with respect to a reference frame, which affects the perceived orientation.
What type of rotation will preserve the orientation of a h-shaped figure in the gird?
Rotation, in the plane of the grid, through 180 degrees.
Is it possible that the orientation of a figure could change after it is translated?
No, translating a figure does not change its orientation. Translation involves moving a figure from one position to another without altering its shape, size, or direction. The figure maintains its original alignment and angles throughout the process.
What transformation always produce a congruent figure?
Reflections, translations, rotations.
Which rigid transformation does NOT result in a reversed orientation of the original image?
A rigid transformation that does not result in a reversed orientation of the original image is a translation or a rotation. Both transformations preserve the orientation of the figure, meaning that the shape and arrangement of points remain unchanged. In contrast, a reflection is the rigid transformation that reverses the orientation.
What transformation is not a congruent image?
A transformation that is not a congruent image is a dilation. Unlike rigid transformations such as translations, rotations, and reflections that preserve shape and size, dilation changes the size of a figure while maintaining its shape. This means that the original figure and the dilated figure are similar, but not congruent, as their dimensions differ.
What is isometry that does not change orientation?
It's a transformation that's order of the letters like ABCD of a figure don't change when transformed.
Which transformation does not produce a congruent image?
A transformation that does not produce a congruent image is a dilation. While dilations change the size of a figure, they maintain the shape, meaning the resulting image is similar but not congruent to the original. In contrast, transformations such as translations, rotations, and reflections preserve both size and shape, resulting in congruent images.
What would be the orientation of the figure L after a translation of 8 units to right and 3 units up?
The orientation of figure L would remain unchanged after a translation of 8 units to the right and 3 units up. Translation moves a figure without altering its shape, size, or direction. Thus, while the position of figure L will change, its orientation will stay the same.
