Dilations Scale Factor Similarity Test – Geometry Math (Printable PDF)

Question 1 Dilate two points (2 points)

Dilate each point about the origin.

1. P(−3, 4) with scale factor 2.5 (1 point)
2. Q(6, −9) with scale factor ⅓ (1 point)

Question 2 Dilate a triangle (3 points)

Triangle DEF has D(2, 1), E(5, 1) and F(2, 5). Dilate it about the origin with scale factor 3 and give the image vertices.

Question 3 Center away from the origin (2 points)

A dilation has center (1, 2) and scale factor 2. Find the image of M(4, 3) (1 point) and of N(−1, 0) (1 point).

Question 4 Properties of dilations (3 points)

A dilation has center O and scale factor 3.

1. A line ℓ does not pass through O. How is its image related to ℓ? (1 point)
2. A line m passes through O. What is the image of m? (1 point)
3. A segment is 9 units long. How long is its image? (1 point)

Question 5 Similar triangle sides (3 points)

△ABC ∼ △DEF. AB = 8, BC = 12, CA = 10 and DE = 20.

1. Find the scale factor from △ABC to △DEF. (1 point)
2. Find EF. (1 point)
3. Find DF. (1 point)

Question 6 AA similarity (3 points)

△PQR has angles m∠P = 48° and m∠Q = 75°. △XYZ has m∠X = 57° and m∠Y = 75°.

1. Find m∠R and m∠Z. (1 point)
2. Are the triangles similar? Name the criterion. (1 point)
3. Write a similarity statement with matching vertices. (1 point)

Question 7 Dilation then translation (2 points)

Triangle ABC with A(0, 0), B(3, 0) and C(0, 4) is mapped onto A′(−2, 1), B′(4, 1) and C′(−2, 9). Find the scale factor of the dilation about the origin (1 point) and the translation that follows (1 point).

Question 8 Flagpole shadow (2 points)

A 1.5-meter stick casts a shadow of 1.2 meters. At the same time a flagpole casts a shadow of 9.6 meters. Write the ratio that relates the triangles (1 point) and find the height of the flagpole (1 point).