Dilations from any center, and what a dilation does to lines

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Ren dilates a rocket sticker by scale factor 3 about its corner C(2, -1). Another corner D is at (5, 3). Where is D′?

   • (8, 6)
   • (9, 12)
   • (11, 11)
   • (15, 9)
2. 2.

   First factor 2, then factor 3. Milo dilates a car sticker by 2 about a center C, then dilates the result by 3 about the same C. What single scale factor does the same job?

   • 3/2
   • 1/6
   • 5
   • 6
3. 3.

   Side AB = 7 cm. Scale factor 3/2. Side AB of Pia's tent flap is 7 cm long. A dilation with scale factor 3/2 is applied. How long is A′B′?

   • 14/3 cm
   • 21/2 cm
   • 7 cm
   • 17/2 cm
4. 4.

   Image side A′B′ = 18 cm. Scale factor 3. A dilation with scale factor 3 makes side A′B′ of Bo's bus picture 18 cm long. How long was AB?

   • 15 cm
   • 6 cm
   • 54 cm
   • 18 cm
5. 5.

   Noah's quilt patch is a square with side 4 cm. A dilation with scale factor 3 is applied. What is the area of the image?

   • 12 cm²
   • 19 cm²
   • 48 cm²
   • 144 cm²
6. 6.

   Tala's star triangle has angles 40°, 60° and 80°. A dilation with scale factor 2 is applied. What are the image's angles?

   • 20°, 30° and 40°, each halved
   • 42°, 62° and 82°, each plus 2
   • 80°, 120° and 160°, each doubled
   • 40°, 60° and 80°, unchanged
7. 7.

   Ari's dilation about the origin has scale factor 3. It sends D(1, 2) to D′(3, 6) and F(2, 1) to F′(6, 3). How does line D′F′ compare with line DF?

   • A line with slope -3, because the dilation multiplies slopes by 3
   • The same line, because the slope is the same
   • A line that crosses DF at the origin
   • A different line, parallel to DF, because DF misses the center
8. 8.

   Line ℓ is y = 2x. It passes through Esme's center, the origin. The dilation has scale factor 3. What is the image of ℓ?

   • The same line, y = 2x
   • y = 2x + 3
   • y = 6x
   • y = 2x + 6, a parallel line, since dilations move lines
9. 9.

   Line m is y = 2x + 1. Jun dilates m by scale factor 3 about the origin. What is the image of m?

   • y = 2x + 3
   • y = 2x + 4
   • y = 6x + 3
   • y = 2x + 1
10. 10.

    A dilation about corner C sends Zee's corner D to D′. Using the coordinates on the card, what is the scale factor?

    • 4
    • 1/3
    • 2
    • 3