Rotation (B) Worksheet | Cazoom Maths Worksheets - Free Printable

To solve the rotation problems, we need to apply the rules of rotation for each given scenario. Here's a step-by-step explanation for each problem:

1) Rotate 180° about the point (-3, 1)

- Rule for 180° rotation about a point \((a, b)\):
\[
(x', y') = (2a - x, 2b - y)
\]
- Vertices of the triangle:
- \((-5, 3)\)
- \((-4, 2)\)
- \((-3, 2)\)

- Apply the rule:
- For \((-5, 3)\):
\[
(x', y') = (2(-3) - (-5), 2(1) - 3) = (-6 + 5, 2 - 3) = (-1, -1)
\]
- For \((-4, 2)\):
\[
(x', y') = (2(-3) - (-4), 2(1) - 2) = (-6 + 4, 2 - 2) = (-2, 0)
\]
- For \((-3, 2)\):
\[
(x', y') = (2(-3) - (-3), 2(1) - 2) = (-6 + 3, 2 - 2) = (-3, 0)
\]

- New vertices:
- \((-1, -1)\)
- \((-2, 0)\)
- \((-3, 0)\)

2) Rotate 90° clockwise about the point (4, -6)

- Rule for 90° clockwise rotation about a point \((a, b)\):
\[
(x', y') = (a + (y - b), b - (x - a))
\]
- Vertices of the rectangle:
- \((2, -4)\)
- \((2, -6)\)
- \((4, -6)\)
- \((4, -4)\)

- Apply the rule:
- For \((2, -4)\):
\[
(x', y') = (4 + (-4 - (-6)), -6 - (2 - 4)) = (4 + 2, -6 + 2) = (6, -4)
\]
- For \((2, -6)\):
\[
(x', y') = (4 + (-6 - (-6)), -6 - (2 - 4)) = (4 + 0, -6 + 2) = (4, -4)
\]
- For \((4, -6)\):
\[
(x', y') = (4 + (-6 - (-6)), -6 - (4 - 4)) = (4 + 0, -6 + 0) = (4, -6)
\]
- For \((4, -4)\):
\[
(x', y') = (4 + (-4 - (-6)), -6 - (4 - 4)) = (4 + 2, -6 + 0) = (6, -6)
\]

- New vertices:
- \((6, -4)\)
- \((4, -4)\)
- \((4, -6)\)
- \((6, -6)\)

3) Rotate 90° anticlockwise about the point (3, 3)

- Rule for 90° anticlockwise rotation about a point \((a, b)\):
\[
(x', y') = (a - (y - b), b + (x - a))
\]
- Vertices of the parallelogram:
- \((1, 2)\)
- \((3, 2)\)
- \((4, 3)\)
- \((2, 3)\)

- Apply the rule:
- For \((1, 2)\):
\[
(x', y') = (3 - (2 - 3), 3 + (1 - 3)) = (3 + 1, 3 - 2) = (4, 1)
\]
- For \((3, 2)\):
\[
(x', y') = (3 - (2 - 3), 3 + (3 - 3)) = (3 + 1, 3 + 0) = (4, 3)
\]
- For \((4, 3)\):
\[
(x', y') = (3 - (3 - 3), 3 + (4 - 3)) = (3 + 0, 3 + 1) = (3, 4)
\]
- For \((2, 3)\):
\[
(x', y') = (3 - (3 - 3), 3 + (2 - 3)) = (3 + 0, 3 - 1) = (3, 2)
\]

- New vertices:
- \((4, 1)\)
- \((4, 3)\)
- \((3, 4)\)
- \((3, 2)\)

4) Rotate 180° about the origin

- Rule for 180° rotation about the origin:
\[
(x', y') = (-x, -y)
\]
- Vertices of the trapezoid:
- \((-5, 4)\)
- \((-4, 4)\)
- \((-3, 1)\)
- \((-5, 1)\)

- Apply the rule:
- For \((-5, 4)\):
\[
(x', y') = (5, -4)
\]
- For \((-4, 4)\):
\[
(x', y') = (4, -4)
\]
- For \((-3, 1)\):
\[
(x', y') = (3, -1)
\]
- For \((-5, 1)\):
\[
(x', y') = (5, -1)
\]

- New vertices:
- \((5, -4)\)
- \((4, -4)\)
- \((3, -1)\)
- \((5, -1)\)

5) Rotate 90° anticlockwise about the origin

- Rule for 90° anticlockwise rotation about the origin:
\[
(x', y') = (-y, x)
\]
- Vertices of the arrow:
- \((2, -4)\)
- \((3, -4)\)
- \((3, -5)\)
- \((4, -5)\)
- \((4, -6)\)
- \((3, -6)\)
- \((3, -7)\)
- \((2, -7)\)

- Apply the rule:
- For \((2, -4)\):
\[
(x', y') = (4, 2)
\]
- For \((3, -4)\):
\[
(x', y') = (4, 3)
\]
- For \((3, -5)\):
\[
(x', y') = (5, 3)
\]
- For \((4, -5)\):
\[
(x', y') = (5, 4)
\]
- For \((4, -6)\):
\[
(x', y') = (6, 4)
\]
- For \((3, -6)\):
\[
(x', y') = (6, 3)
\]
- For \((3, -7)\):
\[
(x', y') = (7, 3)
\]
- For \((2, -7)\):
\[
(x', y') = (7, 2)
\]

- New vertices:
- \((4, 2)\)
- \((4, 3)\)
- \((5, 3)\)
- \((5, 4)\)
- \((6, 4)\)
- \((6, 3)\)
- \((7, 3)\)
- \((7, 2)\)

6) Rotate 90° clockwise about the origin

- Rule for 90° clockwise rotation about the origin:
\[
(x', y') = (y, -x)
\]
- Vertices of the rectangle:
- \((2, 3)\)
- \((2, 4)\)
- \((5, 4)\)
- \((5, 3)\)

- Apply the rule:
- For \((2, 3)\):
\[
(x', y') = (3, -2)
\]
- For \((2, 4)\):
\[
(x', y') = (4, -2)
\]
- For \((5, 4)\):
\[
(x', y') = (4, -5)
\]
- For \((5, 3)\):
\[
(x', y') = (3, -5)
\]

- New vertices:
- \((3, -2)\)
- \((4, -2)\)
- \((4, -5)\)
- \((3, -5)\)

Final Answer:

\[
\boxed{
\begin{array}{ll}
1) & (-1, -1), (-2, 0), (-3, 0) \\
2) & (6, -4), (4, -4), (4, -6), (6, -6) \\
3) & (4, 1), (4, 3), (3, 4), (3, 2) \\
4) & (5, -4), (4, -4), (3, -1), (5, -1) \\
5) & (4, 2), (4, 3), (5, 3), (5, 4), (6, 4), (6, 3), (7, 3), (7, 2) \\
6) & (3, -2), (4, -2), (4, -5), (3, -5) \\
\end{array}
}
\]