← Back to the Dilations Scale Factor Similarity test
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: G-SRT.A.1, G-SRT.A.2, G-SRT.A.3 · Level: Grade 10 Geometry
Question 1 Dilate two points (2 points)
- (2.5 · (−3), 2.5 · 4) = (−7.5, 10).
- (6 ÷ 3, −9 ÷ 3) = (2, −3).
(a) (−7.5, 10), (b) (2, −3)
Scoring: 1 point per image.
Question 2 Dilate a triangle (3 points)
Multiply each coordinate by 3: D′(6, 3), E′(15, 3), F′(6, 15).
D′(6, 3), E′(15, 3), F′(6, 15)
Scoring: 1 point per vertex.
Question 3 Center away from the origin (2 points)
For M: vector (3, 1), doubled (6, 2), so M′ = (1 + 6, 2 + 2) = (7, 4).
For N: vector (−2, −2), doubled (−4, −4), so N′ = (1 − 4, 2 − 4) = (−3, −2).
M′(7, 4), N′(−3, −2)
Scoring: 1 point per image.
Question 4 Properties of dilations (3 points)
- The image is a line parallel to ℓ.
- The image is m itself.
- 9 × 3 = 27 units.
(a) parallel line, (b) the same line, (c) 27 units
Scoring: 1 point per part.
Question 5 Similar triangle sides (3 points)
- k = DE ÷ AB = 20 ÷ 8 = 2.5.
- EF = 2.5 × 12 = 30.
- DF = 2.5 × 10 = 25.
(a) 2.5, (b) 30, (c) 25
Scoring: 1 point per part.
Question 6 AA similarity (3 points)
- m∠R = 180° − 48° − 75° = 57° and m∠Z = 180° − 57° − 75° = 48°.
- Both triangles have angles 48°, 57° and 75°, so they are similar by AA.
- Match equal angles: P (48°) ↔ Z, Q (75°) ↔ Y, R (57°) ↔ X.
(a) 57° and 48°, (b) similar by AA, (c) △PQR ∼ △ZYX
Scoring: 1 point per part.
Question 7 Dilation then translation (2 points)
AB = 3 and A′B′ = 6, so k = 2. The dilation sends A, B, C to (0, 0), (6, 0), (0, 8). The translation by ⟨−2, 1⟩ gives (−2, 1), (4, 1), (−2, 9).
k = 2; translation by ⟨−2, 1⟩
Scoring: 1 point per part.
Question 8 Flagpole shadow (2 points)
The triangles are similar by AA, so height ÷ shadow is the same: 1.5 ÷ 1.2 = h ÷ 9.6. Then h = 9.6 × 1.5 ÷ 1.2 = 12.
The flagpole is 12 meters tall
Scoring: 1 point for the ratio, 1 point for the height.