Question

name:
reflect across the x axis
rotate 90° counter clockwise
translate 4 up
reflect across the x axis
rotate 180° clockwise

Explanation:

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1. Reflect across the x-axis (Top Left)

Step1: Identify original points

Original triangle \(ABC\): \(A(3, 2)\), \(B(3, -6)\), \(C(1, -6)\)

Step2: Apply x-axis reflection rule

Rule: \((x, y) \to (x, -y)\)
New points:
\(A'(3, -2)\), \(B'(3, 6)\), \(C'(1, 6)\)
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2. Rotate 90° counterclockwise (Top Right)

Step1: Identify original points

Original triangle \(XYZ\): \(X(-2, 3)\), \(Y(-6, 0)\), \(Z(0, 0)\)

Step2: Apply 90° CCW rotation rule

Rule: \((x, y) \to (-y, x)\)
New points:
\(X'(-3, -2)\), \(Y'(0, -6)\), \(Z'(0, 0)\)
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3. Translate 4 units up (Middle Left)

Step1: Identify original points

Original triangle \(JKL\): \(J(3, 2)\), \(K(3, -6)\), \(L(-2, -3)\)

Step2: Apply vertical translation rule

Rule: \((x, y) \to (x, y+4)\)
New points:
\(J'(3, 6)\), \(K'(3, -2)\), \(L'(-2, 1)\)
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4. Reflect across the x-axis (Middle Right)

Step1: Identify original points

Original triangle \(OMN\): \(O(-5, 0)\), \(M(2, -6)\), \(N(4, -3)\)

Step2: Apply x-axis reflection rule

Rule: \((x, y) \to (x, -y)\)
New points:
\(O'(-5, 0)\), \(M'(2, 6)\), \(N'(4, 3)\)
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5. Rotate 180° clockwise (Bottom Left)

Step1: Identify original points

Original triangle \(EFG\): \(E(0, -6)\), \(F(4, 0)\), \(G(4, 2)\)

Step2: Apply 180° rotation rule

Rule: \((x, y) \to (-x, -y)\)
New points:
\(E'(0, 6)\), \(F'(-4, 0)\), \(G'(-4, -2)\)
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6. [No transformation listed for bottom right; if assuming 180° rotation (common practice)]

Step1: Identify original points

Original triangle \(QRS\): \(Q(-2, 8)\), \(R(-6, -4)\), \(S(8, -2)\)

Step2: Apply 180° rotation rule

Rule: \((x, y) \to (-x, -y)\)
New points:
\(Q'(2, -8)\), \(R'(6, 4)\), \(S'(-8, 2)\)
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Answer:

1. Reflected triangle points: \(A'(3, -2)\), \(B'(3, 6)\), \(C'(1, 6)\)
2. Rotated triangle points: \(X'(-3, -2)\), \(Y'(0, -6)\), \(Z'(0, 0)\)
3. Translated triangle points: \(J'(3, 6)\), \(K'(3, -2)\), \(L'(-2, 1)\)
4. Reflected triangle points: \(O'(-5, 0)\), \(M'(2, 6)\), \(N'(4, 3)\)
5. Rotated triangle points: \(E'(0, 6)\), \(F'(-4, 0)\), \(G'(-4, -2)\)
6. (180° rotation) Transformed triangle points: \(Q'(2, -8)\), \(R'(6, 4)\), \(S'(-8, 2)\)

To plot each transformed shape, graph the new points and connect them in order.