Question

1. rotation 90° clockwise about the origin

m(1,2) m( , )
b(3,1) b( , )
f(1,3) f( , )
h(2,1) h( , )

1. rotation 180° about the origin

1. rotation 90° clockwise about the origin

u(1, -2), w(1, 2), k(3, 2), g(3, -2)

1. rotation 180° about the origin

v(2, 6), s(1, 3), g(5, 3)

Explanation:

Step1: Recall Rotation Rules

For a point \((x, y)\):

• Rotation \(90^\circ\) clockwise about the origin: \((x, y) \to (y, -x)\)
• Rotation \(180^\circ\) about the origin: \((x, y) \to (-x, -y)\)

Step2: Solve Problem 5 (90° Clockwise Rotation)

Given points: \(U(1, -2)\), \(W(1, 2)\), \(K(3, 2)\), \(G(3, -4)\)

• For \(U(1, -2)\): Apply \((x, y) \to (y, -x)\) → \(U'(-2, -1)\)
• For \(W(1, 2)\): Apply \((x, y) \to (y, -x)\) → \(W'(2, -1)\)
• For \(K(3, 2)\): Apply \((x, y) \to (y, -x)\) → \(K'(2, -3)\)
• For \(G(3, -4)\): Apply \((x, y) \to (y, -x)\) → \(G'(-4, -3)\)

Step3: Solve Problem 6 (180° Rotation)

Given points: \(V(2, 6)\), \(S(1, 3)\), \(C(5, 3)\)

• For \(V(2, 6)\): Apply \((x, y) \to (-x, -y)\) → \(V'(-2, -6)\)
• For \(S(1, 3)\): Apply \((x, y) \to (-x, -y)\) → \(S'(-1, -3)\)
• For \(C(5, 3)\): Apply \((x, y) \to (-x, -y)\) → \(C'(-5, -3)\)

(Note: For the graph - based rotation problems (like 3 and 4), we would visually identify the rotated vertices using the same rotation rules and plot them, but since coordinates for those are partially hand - written, we focused on the numbered problems with clear coordinates here.)

Answer:

Problem 5 (90° Clockwise Rotation)

\(U'(-2, -1)\), \(W'(2, -1)\), \(K'(2, -3)\), \(G'(-4, -3)\)

Problem 6 (180° Rotation)

\(V'(-2, -6)\), \(S'(-1, -3)\), \(C'(-5, -3)\)