Pregunta
What are the coordinates of the image of the point \( (7,8) \) after a \( 90^{\circ} \) clockwise rotation about the origin? Select one: a. \( (8,-7) \) b. \( (-8,7) \) c. \( (-7,-8) \) d. \( (8,7) \)
Ask by Morrison Grant. in the United States
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The image of the point \((7,8)\) after a \(90^\circ\) clockwise rotation about the origin is \((8,-7)\).
Solución
1. For a \(90^\circ\) clockwise rotation about the origin, the transformation rule is:
\[
(x, y) \rightarrow (y, -x)
\]
2. Given the point \((7,8)\), substitute \(x = 7\) and \(y = 8\) into the rule:
\[
(7,8) \rightarrow (8,-7)
\]
3. Therefore, the coordinates of the image after the rotation are \((8,-7)\).
The correct answer is a. \( (8,-7) \).
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Simplifique esta solución Bonus Knowledge
When a point \( (x, y) \) is rotated \( 90^{\circ} \) clockwise about the origin, its new coordinates become \( (y, -x) \). For the point \( (7, 8) \), applying this transformation gives us the new coordinates \( (8, -7) \). Thus, the correct answer is: a. \( (8,-7) \). In rotation transformations, remember that the direction (clockwise vs. counterclockwise) greatly changes the resulting coordinates. Always double-check the order of the transformations to avoid mistakes!
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