Answer:
A requirement that must be met for a transformation to be a rigid motion is the fact that the shape and size of the image and its preimage (real object) must remain same i.e they must be congruent. Please check the attached figure a.
Another requirement is that the size of a figure can not be increased or decreased when we carry out the rigid transformation. In order to increase or decreases the size, dilation is used to transform the figure.
Step-by-step explanation:
A transformation can be termed as rigid transformation of any plane which is able to preserve the relative distance between the points. Some of the rigid transformations include translation, rotation and reflection and the combinations of them.
While the pre-image and the image under a rigid transformation will be congruent, they may not be facing in the same direction.
A reflection just giving a mirror image of a object, translation just sliding the object, and rotation just turning the object are all rigid transformations as they preserve the shape and size.
A requirement that must be met for a transformation to be a rigid motion is the fact that the shape and size of the image and its preimage (real object) must remain same i.e they must be congruent. Please check the attached figure a.
For example, The reflection of the point P(a, b) across the x-axis is the point P'(a, -b). Only the sign of y-coordinate changes, while x coordinate remains the same.
Another example is that if we want to reflect the triangle ΔABC with the vertices A(-2, 1), B(1, 4) and C(3, 2) across x-axis. Then the reflected ΔA'B'C' will have the vertices A(-2, -1), B(1, -4) and C(3, -2). It is clear that shape and size of image (ΔA'B'C') and its pre-image (ΔABC) remains the same when triangle ΔABC is reflected across x-axis. Please check the attached figure a.
Another requirement is that the size of a figure can not be increased or decreased when we carry out the rigid transformation. In order to increase or decreases the size, dilation is used to transform the figure.
Keywords: rigid transformation
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