Rigid Transformations Test – Geometry Math (Printable PDF)

Question 1 Images of a point (2 points)

Find the image of (−6, 2) under each transformation.

1. Translation by ⟨4, −7⟩ (1 point)
2. Reflection over the y-axis (1 point)

Question 2 Half-turn of a triangle (3 points)

Triangle DEF has D(−5, 1), E(−1, 1) and F(−2, 4). Rotate it 180° about the origin and give the image vertices.

Question 3 Reflect over y = x (3 points)

Reflect G(2, −3), H(5, 0) and K(−4, −1) over the line y = x.

Question 4 Rigid or not (2 points)

Decide whether each rule is a rigid transformation and justify with a segment.

1. (x, y) → (x − 6, y + 5) (1 point)
2. (x, y) → (x/3, y/3) (1 point)

Question 5 Rotation about a center (3 points)

Rotate A(6, 2) by 90° counterclockwise about the center (1, −1). Show the steps and find A′.

Question 6 Symmetry of polygons (3 points)

Answer each part.

1. How many lines of symmetry does a regular 15-gon have? (1 point)
2. What is the smallest positive angle of rotational symmetry of that polygon? (1 point)
3. How many lines of symmetry does a rhombus that is not a square have? (1 point)

Question 7 Order of motions (2 points)

Point A(4, −1) is reflected over the x-axis and then translated by ⟨−3, 7⟩. Find the final point. What is the result when the translation is done first?

Question 8 Name the transformation (2 points)

Triangle JKL with J(−3, 2), K(−3, 6) and L(−1, 6) is mapped onto J′(3, 2), K′(3, 6) and L′(1, 6). Name the single transformation that does this.