Rigid Transformations Test Answer Key with Scoring – Geometry

Question 1 Images of a point (2 points)

1. (−6 + 4, 2 − 7) = (−2, −5).
2. Negate x: (6, 2).

(a) (−2, −5), (b) (6, 2)

Scoring: 1 point per image.

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

Negate both coordinates of each vertex: D′(5, −1), E′(1, −1), F′(2, −4).

D′(5, −1), E′(1, −1), F′(2, −4)

Scoring: 1 point per vertex.

Question 3 Reflect over y = x (3 points)

Swap the coordinates: G′(−3, 2), H′(0, 5), K′(−1, −4).

G′(−3, 2), H′(0, 5), K′(−1, −4)

Scoring: 1 point per point.

Question 4 Rigid or not (2 points)

1. It is a translation. The segment from (1, 1) to (5, 1) goes to (−5, 6)–(−1, 6), still length 4: rigid.
2. It shrinks lengths to a third. The segment from (0, 0) to (6, 0) goes to (0, 0)–(2, 0), length 2: not rigid.

(a) rigid, (b) not rigid

Scoring: 1 point per part, including the justification.

Question 5 Rotation about a center (3 points)

Subtract the center: (6 − 1, 2 − (−1)) = (5, 3). Rotate with (x, y) → (−y, x): (−3, 5). Add the center back: (−3 + 1, 5 + (−1)) = (−2, 4).

A′(−2, 4)

Scoring: 1 point for translating to the origin, 1 point for the rotation, 1 point for the final point.

Question 6 Symmetry of polygons (3 points)

1. A regular n-gon has n lines of symmetry: 15.
2. 360° ÷ 15 = 24°.
3. Only the two diagonals: 2.

(a) 15, (b) 24°, (c) 2

Scoring: 1 point per part.

Question 7 Order of motions (2 points)

Reflect: (4, 1); translate: (1, 8).

Translate first: (1, 6); reflect: (1, −6).

(1, 8), and (1, −6) in the other order

Scoring: 1 point for each final point.

Question 8 Name the transformation (2 points)

Each y-coordinate stays the same and each x-coordinate changes sign, so the rule is (x, y) → (−x, y).

A reflection over the y-axis

Scoring: 1 point for the type of transformation, 1 point for the line or rule.