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

Grade 10 Math Worksheet

Circle the best answer.

1. 1.

   Luz dilates a quilt triangle with corners C(-3, 1), D(1, -3) and E(-1, 3) by scale factor 3/2 about corner C. Where is D′?

   • (3, -5)
   • (3/2, -9/2)
   • (6, -6)
   • (5/2, -3/2)
2. 2.

   Bo dilates segment AB, with A(1, 1) and B(5, 3), by scale factor 2 about A. Which statement about the image is right?

   • A′ = A and B′ = (9, 5); the image lies on line AB and is twice as long
   • A′ = A and B′ = (9, 5); the image is parallel to AB, not on it
   • A′ = A and B′ = (7, 5); B moves 2 across and 2 up from where it began
   • A′ = (2, 2) and B′ = (10, 6); the dilation is about the origin, not about A
3. 3.

   A dilation about the origin has scale factor 3/2. Kira dilates segment AB with A(2, 0), B(6, 4) and its midpoint M(4, 2). Is M′ the midpoint of A′B′?

   • Yes: A′(3, 0), B′(9, 6) and M′(6, 3), and the midpoint of A′B′ is (6, 3)
   • Yes, because a dilation keeps the points where they are
   • No, because a dilation stretches lengths, so a midpoint moves off center
   • No: M′ is (11/2, 7/2), while the midpoint of A′B′ is (6, 3)
4. 4.

   Esme dilates the line y = 3x − 2 by scale factor 2 about the origin. What is the image?

   • y = 3x − 4
   • y = 6x − 4
   • y = 3x − 1
   • y = 3x − 2
5. 5.

   Milo dilates the line y = 2x + 3 by scale factor 3 about C(1, 5). What is the image?

   • y = 2x + 7, a parallel line, because lines move when dilated
   • The same line, y = 2x + 3, because C(1, 5) is on it
   • y = 6x + 3, because the slope doubles
   • y = 2x + 9, because the intercept triples
6. 6.

   Noah dilates the line y = 2x + 3 by scale factor 1/2 about the origin. What is the image?

   • y = x + 3/2
   • y = 2x + 6
   • y = 2x + 3
   • y = 2x + 3/2
7. 7.

   A dilation about the origin sends Pia's line y = 2x + 4 to the line y = 2x + 10. What is the scale factor?

   • 6
   • 14
   • 2/5
   • 5/2
8. 8.

   Image area 72 cm². Scale factor 3. Zee's snowman sign becomes 72 cm² in area after a dilation with scale factor 3. What was the original area?

   • 24 cm²
   • 216 cm²
   • 8 cm²
   • 72 cm²
9. 9.

   First factor 2, then factor 3/2. Jun dilates a castle picture by 2 about C, then by 3/2 about the same C. What single scale factor does the same job?

   • 7/2
   • 6
   • 3
   • 4/3
10. 10.

    Esme dilates a triangle with corners P(4, 4), Q(8, 0) and R(8, 4) by scale factor 1/2 about corner P. Where is Q′, and is it closer to P or farther?

    • Q′ = (4, 0), closer to P than Q
    • Q′ = (6, 2), closer to P than Q
    • Q′ = (6, 2), the same distance from P as Q
    • Q′ = (12, -4), farther from P than Q