50+ Rotations worksheets for 8th Grade on Quizizz | Free & Printable - Free Printable

Problem Analysis and Solution

The provided worksheet focuses on rotations and dilations in the coordinate plane. Let's solve each problem step by step.

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#### Question 1: What is the rule for rotating a figure 90 degrees counterclockwise?

- Rotation Rule: When a point \((x, y)\) is rotated 90 degrees counterclockwise about the origin, the new coordinates become \((-y, x)\).
- Explanation:
- The \(x\)-coordinate becomes the negative of the original \(y\)-coordinate.
- The \(y\)-coordinate becomes the original \(x\)-coordinate.

- Correct Answer: B. \((-y, x)\)

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#### Question 2: What is the rule for rotating a figure 180 degrees?

- Rotation Rule: When a point \((x, y)\) is rotated 180 degrees about the origin, the new coordinates become \((-x, -y)\).
- Explanation:
- Both the \(x\)-coordinate and the \(y\)-coordinate are negated.

- Correct Answer: C. \((-x, -y)\)

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#### Question 3: Rotate the point \((5, 5)\) around the origin 180 degrees. State the image of the point.

- Given Point: \((5, 5)\)
- Rotation Rule for 180 Degrees: \((x, y) \rightarrow (-x, -y)\)
- Application:
- Original coordinates: \((5, 5)\)
- New coordinates: \((-5, -5)\)

- Correct Answer: D. \((-5, -5)\)

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#### Question 4: What is the rule for rotating a figure 270 degrees counterclockwise?

- Rotation Rule: When a point \((x, y)\) is rotated 270 degrees counterclockwise about the origin, the new coordinates become \((y, -x)\).
- Explanation:
- The \(x\)-coordinate becomes the original \(y\)-coordinate.
- The \(y\)-coordinate becomes the negative of the original \(x\)-coordinate.

- Correct Answer: C. \((y, -x)\)

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#### Question 5: If you were to rotate ABCD 180° about the origin, what would the coordinate of \(A'\) be?

- Given Figure: The figure shows a rectangle \(ABCD\) with vertex \(A\) at \((3, 5)\).
- Rotation Rule for 180 Degrees: \((x, y) \rightarrow (-x, -y)\)
- Application:
- Original coordinates of \(A\): \((3, 5)\)
- New coordinates of \(A'\): \((-3, -5)\)

- Correct Answer: A. \((-3, -5)\)

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#### Question 6: State the coordinate of the image of the given point \(B(-10, -6)\) under a dilation with center at the origin and the given scale factor \(k = \frac{1}{2}\).

- Given Point: \(B(-10, -6)\)
- Dilation Rule: For a dilation with center at the origin and scale factor \(k\), the new coordinates are \((kx, ky)\).
- Scale Factor: \(k = \frac{1}{2}\)
- Application:
- Original coordinates: \((-10, -6)\)
- New coordinates: \(\left(\frac{1}{2} \cdot (-10), \frac{1}{2} \cdot (-6)\right) = (-5, -3)\)

- Correct Answer: \((-5, -3)\)

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Final Answers:

1. B. \((-y, x)\)
2. C. \((-x, -y)\)
3. D. \((-5, -5)\)
4. C. \((y, -x)\)
5. A. \((-3, -5)\)
6. \((-5, -3)\)

Boxed Final Answer:
\[
\boxed{B, C, D, C, A, (-5, -3)}
\]