Suppose a preimage is dilated by a scale factor of 3 and rotated 270° counterclockwise. Is the resulting image similar to the preimage?

Question

(1 point)
Responses

Yes, because rotations preserve angle measure, but not segment length.
Yes, because rotations preserve angle measure, but not segment length.

Yes, because dilations preserve angle measure, but not segment length.
Yes, because dilations preserve angle measure, but not segment length.

No, because rotations preserve neither angle measure nor segment length.
No, because rotations preserve neither angle measure nor segment length.

No, because dilations do not preserve angle measure, but do preserve segment length.

Answer 1

The correct response is:

Yes, because dilations preserve angle measure, but not segment length.

Here's the reasoning:

1. A dilation by a scale factor (in this case, 3) enlarges the figure but preserves the shape. This means that the angles remain the same, but the lengths of the segments are multiplied by the scale factor.
2. A rotation (in this case, 270° counterclockwise) also preserves angles and the shapes, but it alters the orientation of the figure.

Since both transformations (dilation and rotation) preserve angle measure, the resulting image will be similar to the preimage.