Pregunta
A square is plotted on a coordinate plane. Henry claims that any transformation on the square will preserve the length of its sides.
Which of the following transformations could be used to show that Henry’s claim is incorrect? Select all that apply.
translation of 5 units to the right
horizontal stretch by a factor of
dilation by a factor of 2 through the origin
rotation of
a reflection over the
Which of the following transformations could be used to show that Henry’s claim is incorrect? Select all that apply.
translation of 5 units to the right
horizontal stretch by a factor of
dilation by a factor of 2 through the origin
rotation of
a reflection over the
Ask by Mccarthy Young. in the United States
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The transformations that change the square’s side lengths are:
- Horizontal stretch by a factor of
- Dilation by a factor of 2 through the origin
Solución
To determine which transformations could disprove Henry’s claim that any transformation on a square preserves the length of its sides, let’s analyze each option:
-
Translation of 5 units to the right:
- Effect: Moves the square without altering its shape or size.
- Conclusion: Preserves side lengths.
-
Horizontal stretch by a factor of
: - Effect: Compresses the square horizontally, reducing the length of the sides in the horizontal direction.
- Conclusion: Does not preserve side lengths.
-
Dilation by a factor of 2 through the origin:
- Effect: Scales the square uniformly, increasing the length of all sides by a factor of 2.
- Conclusion: Does not preserve side lengths.
-
Rotation of
clockwise about the square’s center: - Effect: Rotates the square without changing its size or shape.
- Conclusion: Preserves side lengths.
-
Reflection over the
-axis: - Effect: Flips the square over the
-axis without altering its size or shape. - Conclusion: Preserves side lengths.
- Effect: Flips the square over the
Transformations that change the lengths of the square’s sides are the horizontal stretch by a factor of
Final Answer:
• A horizontal stretch by a factor of
• Dilation by a factor of 2 through the origin
• Dilation by a factor of 2 through the origin
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Simplifique esta solución Beyond the Answer
Henry’s claim can be challenged by certain transformations that change the dimensions of the square. The horizontal stretch by a factor of
On the other hand, transformations like translation, rotation, or reflection do not affect the lengths of the sides of the square. They merely reposition or reorient the square without stretching, shrinking, or altering its dimensions in a way that affects the lengths.
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