Question

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△DEF is rotated about point N to △D′E′F′ .

Which statements are true about the pre-image and image?

Select each correct answer.


DN¯¯¯¯¯¯≅D′N′¯¯¯¯¯¯¯¯

All corresponding points on the image and pre-image are equidistant to point N.

The image is the same size and shape as the pre-image.

The corresponding side lengths in the image and the pre-image are not equal.

Answer 1

△DEF is rotated about point N to △D′E′F′.

A rotation is a transformation that turns a figure about a fixed point called the center of rotation. In your case the center of rotation is point N. A rotation is an isometric transformation: the original figure and the image are congruent. Main properties of rotation:

1) A rotation preserves lengths of segments.

2) A rotation preserves degrees of angles.

3) A rotation maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.

Therefore, option C is true (because the original figure and the image are congruent) and option D is false (because the original figure and the image must be congruent).

All corresponding points on the image and pre-image are equidistant to point N. This option is true (because rotation preserves lengths of segments), thus, DN≅D'N'.