Question

Which of the following transformations could be employed to demonstrate that Henry's assertion, claiming the preservation of the length of a square's sides under any transformation, is incorrect? Choose TWO options from the given possibilities:

A. Translation of 5 units to the right
B. Horizontal stretch by a factor of 13
C. Dilation by a factor of 2 through the origin
D. Rotation of 45° clockwise about the square's center

Answer 1

The transformations that would demonstrate the incorrectness of Henry's assertion by not preserving the length of a square's sides are a horizontal stretch by a factor of 13 and a dilation by a factor of 2 through the origin. The correct answer is B. Horizontal stretch by a factor of 13.

Step-by-step explanation:

To demonstrate that Henry's assertion about a square's sides preserving their length under any transformation is incorrect, we must select transformations that alter the side lengths. Out of the options provided, two specific transformations will change the side lengths:

• Horizontal stretch by a factor of 13: This will multiply the length of each side of the square that is parallel to the horizontal axis by 13, clearly altering the original length.
• Dilation by a factor of 2 through the origin: This will multiply the length of each side of the square by 2, doubling the original length and thus changing the measurement of the sides.

It's essential to note that translations and rotations do not change the lengths of a shape's sides; they only reposition the shape in the plane. Therefore, options A (translation) and D (rotation) would not disprove Henry's assertion as they preserve the side lengths.