Add, subtract and scale vectors

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. Read this first

   Use this

   Grid mat. East is the positive run and north is the positive rise. The robot starts at (0, 0), slides u to P, then slides v from P to Q.

2. 1.

   Ari's robot slides u = ⟨4, 1⟩ across the mat, then v = ⟨-1, 3⟩ from where it stopped. Which single slide from the start gives the same finish?

   • ⟨5, 4⟩
   • ⟨5, 2⟩
   • ⟨5, -2⟩
   • ⟨3, 4⟩
3. 2.

   Jun walks 3 blocks east, then 4 blocks east. A friend walks 3 blocks east, then 4 blocks north. How far from the start does each end?

   • Both end 7 blocks away, since 3 + 4 = 7
   • Jun ends 5 blocks away; the friend ends 7 blocks away
   • Jun ends 7 blocks away; the friend ends 5 blocks away
   • Jun ends 7 blocks away; the friend ends 25 blocks away
4. 3.

   Kira's drone flies v = ⟨3, 4⟩ km. A second flight is -2v. Which describes the second flight's length and direction?

   • 10 km long, in the same direction as v
   • 10 km long, in the opposite direction
   • 5 km long, in the opposite direction
   • 14 km long, in the opposite direction
5. 4.

   Luz's toy rocket moves w = ⟨4, -6⟩ cm on the screen. A half push moves it ½w. Which move is ½w?

   • ⟨-2, 3⟩
   • ⟨2, -3⟩
   • ⟨8, -12⟩
   • ⟨2, -6⟩
6. 5.

   Stops measured from home at the origin. Milo's bike stops are measured from home: stop 1 is ⟨2, 3⟩ km, stop 2 is ⟨6, 9⟩ km. Is stop 3 at ⟨10, 14⟩ km on the same straight line from home?

   • Yes: each stop is farther east and north, so the line keeps going
   • Yes: 10 is 5 times 2, so ⟨10, 14⟩ is 5 times ⟨2, 3⟩
   • No: stop 2 is 3 times stop 1, but ⟨10, 14⟩ is not a multiple of ⟨2, 3⟩
   • Yes: from stop 2 to stop 3 adds ⟨4, 5⟩, close to the earlier steps
7. 6.

   Pia's snail crawls ⟨5, 12⟩ cm. A second crawl goes the same way and is 3 times as long. How long is the second crawl?

   • 16 cm
   • 507 cm
   • 51 cm
   • 39 cm
8. 7.

   Ren's tent is at A(2, 1) on a map in km and the campfire is at B(7, 4). Which vector is the walk from the tent to the campfire?

   • ⟨5, 3⟩
   • ⟨9, 5⟩
   • ⟨5, -3⟩
   • ⟨-5, -3⟩
9. 8.

   Tala's map shows the school at S(1, -2) and the library at L(-3, 4). Which vector is the route from the school to the library?

   • ⟨-4, 2⟩
   • ⟨-2, 2⟩
   • ⟨4, -6⟩
   • ⟨-4, 6⟩
10. 9.

    Zee's toy car sits at u = ⟨6, 2⟩ at noon and v = ⟨1, 5⟩ at one o'clock, both measured from home. What does v − u tell Zee?

    • Just how many centimeters apart the two spots are, with no direction
    • The slide that carries the car from its one o'clock spot back to its noon spot
    • The total slide if the car first goes to u and then goes v farther
    • The slide that carries the car from its noon spot to its one o'clock spot
11. 10.

    Noah's quilt piece is a parallelogram with sides u = ⟨3, 0⟩ and v = ⟨1, 2⟩ from corner A. Which vector runs from A to the opposite corner C?

    • ⟨2, -2⟩, the difference u − v
    • ⟨-2, 2⟩, the difference v − u
    • ⟨4, 2⟩, the sum u + v
    • ⟨8, 4⟩, twice the sum