Three Step Transformations (A) - Free Printable

1) Translation (1,4): Move each vertex of triangle ABC right 1 unit and up 4 units. New points: A'(2,5), B'(0,6), C'(0,4).
Reflection y = -3: Reflect each translated point across the horizontal line y = -3. For any point (x,y), its reflection is (x, -6 - y). New points: A''(2,-11), B''(0,-12), C''(0,-10).
Rotation 180°, center R(3,2): Rotate each reflected point 180° around (3,2). The formula is (x,y) → (6-x, 4-y). Final points: A'''(4,15), B'''(6,16), C'''(6,14).

2) Dilation scale = -1/2, center D(4,2): Multiply the vector from D to each vertex by -1/2. A(5,0) → A'(3.5,3); B(1,0) → B'(5.5,3); C(1,2) → C'(5.5,2).
Reflection x = 1: Reflect each dilated point across the vertical line x = 1. For any point (x,y), its reflection is (2-x, y). New points: A''(-1.5,3), B''(-3.5,3), C''(-3.5,2).
Translation (3,2): Move each reflected point right 3 units and up 2 units. Final points: A'''(1.5,5), B'''(-0.5,5), C'''(-0.5,4).

3) Dilation scale = 1/4, center D(3,3): Multiply the vector from D to each vertex by 1/4. A(7,0) → A'(4,2.25); B(1,6) → B'(3.5,4.5); C(-1,0) → C'(2,2.25).
Translation (3,2): Move each dilated point right 3 units and up 2 units. New points: A''(7,4.25), B''(6.5,6.5), C''(5,4.25).
Reflection y = 3: Reflect each translated point across the horizontal line y = 3. For any point (x,y), its reflection is (x, 6-y). Final points: A'''(7,1.75), B'''(6.5,-0.5), C'''(5,1.75).

4) Translation (-2,3): Move each vertex of triangle ABC left 2 units and up 3 units. New points: A'(-1,5), B'(0,3), C'(-2,3).
Rotation 30° counterclockwise, center R(2,0): Use rotation formula for 30° around (2,0): (x,y) → (2 + (x-2)cos30° - y sin30°, 0 + (x-2)sin30° + y cos30°). Approximate cos30°≈0.866, sin30°=0.5.
A'(-1,5) → A''(2 + (-3)(0.866) - 5(0.5), 0 + (-3)(0.5) + 5(0.866)) ≈ (2 - 2.598 - 2.5, -1.5 + 4.33) ≈ (-3.098, 2.83)
B'(0,3) → B''(2 + (-2)(0.866) - 3(0.5), 0 + (-2)(0.5) + 3(0.866)) ≈ (2 - 1.732 - 1.5, -1 + 2.598) ≈ (-1.232, 1.598)
C'(-2,3) → C''(2 + (-4)(0.866) - 3(0.5), 0 + (-4)(0.5) + 3(0.866)) ≈ (2 - 3.464 - 1.5, -2 + 2.598) ≈ (-2.964, 0.598)
Reflection y = 0: Reflect each rotated point across the x-axis. For any point (x,y), its reflection is (x, -y). Final points: A'''(-3.098, -2.83), B'''(-1.232, -1.598), C'''(-2.964, -0.598).

5) Translation (1,0): Move each vertex of triangle ABC right 1 unit. New points: A'(0,0), B'(-1,3), C'(0,5).
Rotation 180°, center R(2,-1): Rotate each translated point 180° around (2,-1). Formula: (x,y) → (4-x, -2-y).
A'(0,0) → A''(4, -2)
B'(-1,3) → B''(5, -5)
C'(0,5) → C''(4, -7)
Reflection x = 4: Reflect each rotated point across the vertical line x = 4. For any point (x,y), its reflection is (8-x, y). Final points: A'''(4, -2), B'''(3, -5), C'''(4, -7).

6) Rotation 90° counterclockwise, center R(3,0): Rotate each vertex 90° CCW around (3,0). Formula: (x,y) → (3 - y, x - 3).
A(6,-2) → A'(5, 3)
B(3,6) → B'(-3, 0)
C(0,0) → C'(3, -3)
Translation (1,4): Move each rotated point right 1 unit and up 4 units. New points: A''(6,7), B''(-2,4), C''(4,1).
Reflection x = 1: Reflect each translated point across the vertical line x = 1. For any point (x,y), its reflection is (2-x, y). Final points: A'''(-4,7), B'''(4,4), C'''(-2,1).