Similar Figures Test Answer Key with Scoring – Grade 8

Question 1 Dilate two points (2 points)

(a) (−6 · 1/3, 9 · 1/3) = (−2, 3)

(b) (4 · 3, −5 · 3) = (12, −15)

Scoring: 1 point per part.

Question 2 Dilate a triangle (3 points)

(a) A′(4, 2), B′(10, 2), C′(4, 6).

(b) AB = 3 and A′B′ = 6, so the ratio is 2 : 1.

Scoring: part (a) 2 points for all three vertices (1 point if two are correct); part (b) 1 point.

Question 3 Recover the factor (3 points)

(a) 10 ÷ 4 = 2.5 and 15 ÷ 6 = 2.5. 2.5

(b) (−2 · 2.5, 8 · 2.5) = (−5, 20)

(c) 8 · 2.5 = 20 units

Scoring: 1 point per part.

Question 4 Congruent triangles (3 points)

(a) Reflect across the x-axis: J(2, 2) → (2, −2); K(6, 2) → (6, −2); L(2, 5) → (2, −5). Translate 7 units left and 1 unit up: (−5, −1), (−1, −1), (−5, −4).

Reflection across the x-axis, then a translation 7 left and 1 up

(b) Yes, because rigid motions map one onto the other.

Scoring: part (a) 1 point per correct move; part (b) 1 point.

Question 5 Similar rectangles (3 points)

(a) 9 ÷ 6 = 3/2 and 12 ÷ 8 = 3/2, so the sides are proportional and all angles are 90°. Yes, with scale factor 3/2 from Q to P

(b) Perimeter of P: 2(9 + 12) = 42 cm. Perimeter of Q: 2(6 + 8) = 28 cm. 42 ÷ 28 = 3/2.

Scoring: part (a) 1 point for the ratios, 1 point for the conclusion; part (b) 1 point.

Question 6 Missing side (2 points)

Scale factor: 10 ÷ 14 = 5/7, and 15 ÷ 21 = 5/7.

x = 28 · 5/7 = 20.

x = 20

Scoring: 1 point for the scale factor, 1 point for the value of x.

Question 7 Dilated segment (2 points)

(a) U′ = (6, 9) and V′ = (−12, 3).

(b) UV = √(12² + 4²) = √160 = 4√10 and U′V′ = √(18² + 6²) = √360 = 6√10. U′V′ is 3/2 times as long as UV, the scale factor.

Scoring: 1 point per part.

Question 8 Toy car model (2 points)

9 · 48 = 432 in., and 432 ÷ 12 = 36.

36 ft

Scoring: 1 point for 432 in., 1 point for converting to feet.