Transformations Test Answer Key with Scoring – Grade 8

Question 1 Points on the plane (2 points)

(a) (−3 + 6, 5 − 8) = (3, −3)

(b) (−3, 5) → (−3, −5)

Scoring: 1 point per part.

Question 2 Rotations of a point (3 points)

(a) (−y, x) = (6, 4)

(b) (−x, −y) = (−4, 6)

(c) (y, −x) = (−6, −4)

Scoring: 1 point per image.

Question 3 Identify the motion (3 points)

(a) A(1, 2) maps to A′(−2, 1) and B(5, 2) to B′(−2, 5): a rotation of 90° counterclockwise about the origin.

(b) (x, y) → (−y, x). Check with C(1, 4) → (−4, 1).

(c) Any two of: side lengths, angle measures, area, parallel sides. For example, AB = 4 and A′B′ = 4; the right angle at A stays a right angle at A′.

Scoring: 1 point per part.

Question 4 Rigid motion properties (2 points)

(a) Rotations preserve lengths and angles. Since 6² + 8² = 10², the largest angle is 90°. Sides 6 in., 8 in., 10 in.; largest angle 90°

(b) Yes: a rotation is a rigid motion, so the image has the same size and shape.

Scoring: 1 point per part.

Question 5 Two moves on a quadrilateral (3 points)

(a) Change the sign of each y: P′(−5, 1), Q′(−1, 1), R′(−2, −3), S′(−5, −2).

(b) Add 7 to x and 3 to y: P″(2, 4), Q″(6, 4), R″(5, 0), S″(2, 1).

Scoring: 1 point for part (a). Part (b): 1 point for using the translation rule correctly, 1 point for all four correct vertices.

Question 6 Find the rule (2 points)

Both coordinates change sign, so the rule is (x, y) → (−x, −y).

Rotation of 180° about the origin; (x, y) → (−x, −y)

Scoring: 1 point for the name, 1 point for the rule.

Question 7 Does order matter? (2 points)

Program A: (−2, 5) → (−5, −2) → (−1, −2).

Program B: (−2, 5) → (2, 5) → (−5, 2).

A ends at (−1, −2); B ends at (−5, 2)

Scoring: 1 point per program.

Question 8 Robotics mat (3 points)

(a) (−5, 3) → (5, 3) → (−5, −3) → (−5 + 4, −3 − 6) = (−1, −9)

(b) After two steps (−5, 3) lands on (−5, −3): a reflection across the x-axis.

Scoring: part (a) 1 point for the two reflections and rotation, 1 point for the translation; part (b) 1 point.