📐 Part 1: Transformation Vocabulary and Concepts

1. Match each transformation with its correct description:

Translation

Turning a shape around a point

Reflection

Sliding a shape to a new position

Rotation

Flipping a shape across a mirror line

2. Which properties stay the same (invariant) when a shape is transformed? Check all that apply:

Side lengths

Angles

Position on the coordinate plane

Shape size

3. A triangle has vertices at A(3,2), B(5,2), and C(4,4). If it is translated by the vector (-2, +3), what are the new coordinates?

A' = ( ____ , ____ ) B' = ( ____ , ____ ) C' = ( ____ , ____ )

📊 Part 2: Coordinate Transformations

4. A square has vertices at P(1,1), Q(3,1), R(3,3), and S(1,3). Complete the table showing coordinates after each transformation:

Transformation	P'	Q'	R'	S'
Reflection across y-axis	( ___ , ___ )	( ___ , ___ )	( ___ , ___ )	( ___ , ___ )
90° clockwise rotation about origin	( ___ , ___ )	( ___ , ___ )	( ___ , ___ )	( ___ , ___ )

5. On the coordinate grid below, plot triangle ABC with vertices A(2,1), B(4,3), and C(2,5). Then draw the triangle after a 180° rotation about the origin and label the new vertices A', B', C'.

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6. Describe the transformation that moves triangle DEF at D(-3,2), E(-1,2), F(-2,4) to triangle D'E'F' at D'(3,2), E'(1,2), F'(2,4):

🔄 Part 3: Sequence of Transformations

7. A rectangle has vertices at W(1,2), X(4,2), Y(4,4), and Z(1,4). It undergoes the following sequence of transformations:

Step 1: Translate by vector (3, -1)

Step 2: Reflect across the x-axis

Calculate the final coordinates:

After Step 1:

W₁ = ( ____ , ____ ) X₁ = ( ____ , ____ ) Y₁ = ( ____ , ____ ) Z₁ = ( ____ , ____ )

After Step 2 (Final position):

W₂ = ( ____ , ____ ) X₂ = ( ____ , ____ ) Y₂ = ( ____ , ____ ) Z₂ = ( ____ , ____ )

8. A designer is creating a pattern using transformations. Starting with shape M, they apply a 270° clockwise rotation about the origin, followed by a translation of (-2, +4). If the original shape had a vertex at (5, -1), what is the final position of this vertex?

9. Explain in your own words why the area of a shape remains the same after any combination of translations, reflections, and rotations: