Question

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A square of perimeter 8 undergoes different rigid transformations. Select all the characteristics of the resulting Image that apply:

•Its perimeter is 8
•Its perimeter is 4
•It is congruent with the preimage.
•Its area is 16
•Its area is 4
•Its side is 4

Answer 1

The resulting image of the square after rigid transformations has a perimeter of 8, is congruent to the preimage, has an area of 16, and has a side length of 4.

Step-by-step explanation:

The characteristics of the resulting image of a square after undergoing rigid transformations are:

• Its perimeter is 8: The perimeter remains the same after transformations.
• It is congruent with the preimage: The image is congruent to the original square.
• Its area is 16: The area of the resulting image is 16 square units.
• Its side is 4: The side length of the resulting square is 4 units.

Answer 2

3 Answers:

• Choice A
• Choice C
• Choice E

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Step-by-step explanation:

The term "rigid transformations" is the same as "isometries".

The three types of such transformations are:

• translation (aka shifting)
• rotation
• reflection

Doing any of these will keep the same area, perimeter, size, distance, etc. The figure will not change. Only its position will, or its orientation.

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Since the perimeter doesn't change, it stays at 8. Therefore, choice A is one of the answers. This rules out choice B.

Choice C is another answer because the figure is identical to its preimage counterpart.

If the perimeter of the square is 8, then its side length would be s = P/4 = 8/4 = 2 units. That leads to an area of s^2 = 2^2 = 4 square units. This points to choice E being another answer and it rules out choice D.

Choice F is false because the side length is 2 units, not 4 units. Also note how P = 4s = 4*4 = 16 would be the perimeter for a square of side length 4.