Which of the following transformations will never produce a congruent figure?
A. rotation
B. reflection
C. translation
D. dilation <------
All of these can produce a congruent figure, depending on the parameters.
Rotations and translations ALWAYS produce a congruent figure.
Reflection produces a congruent figure if the object has at least one line of symmetry.
Images of dilations are mostly not congruent with the original object, EXCEPT when the scale parameter is equal to 1 or -1.
If you have to choose one, dilation would be a most probable choice.
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Dialation
reflection followed by a translation
To determine which of the transformations will never produce a congruent figure, we need to understand the properties of each transformation.
A. Rotation: A rotation is a transformation that turns a figure around a fixed point called the center of rotation. Since a rotation does not change the size or shape of the figure, it can produce a congruent figure.
B. Reflection: A reflection is a transformation that flips a figure over a line called the line of reflection. Like a rotation, a reflection does not change the size or shape of the figure, so it can produce a congruent figure.
C. Translation: A translation is a transformation that moves a figure without changing its size or shape. It simply slides the figure in a particular direction. Again, since the size and shape remain the same, a translation can produce a congruent figure.
D. Dilation: A dilation is a transformation that changes the size of a figure. It enlarges or reduces the figure by a scale factor. Since a dilation changes the size, it will never produce a congruent figure.
Therefore, the transformation that will never produce a congruent figure is D. dilation.