Question

Which sequence of transformations does not preserve distance and angle? rotation and reflection

translation and reflection
rotation and dilation

Answer 1

C. Rotation and dilation.

Explanation:

We are asked to choose the sequence of transformations that does not preserve distance and angle from our given choices.

Since we know that preserving distance means if the length of a segment is 5 units, then it will be 5 units after the transformation. Preserving angle means that if the measure of an angle is x degrees, then it will be x degrees after the transformation as well.

The transformations that preserve distance and angle are known as rigid transformations. Translation, rotation and reflection are rigid transformation, while dilation is non rigid transformation.

Therefore, rotation and dilation will not preserve distance and angle as dilation enlarges or compresses a figure.

Answer 2

Answer: rotation and dilation.

While rotation only rotates (obviously) the figure, dilation preserves the shape of the figure (that is, preserves the angles) but changes the distances: it makes the figure smaller.

The other 2 sequences of transformations only change the position of the figure, but the angles and distances remain intact.