The distance formula

Grade 10 Math Worksheet

Circle the best answer.

1. 1.

   Pia plots quadrilateral ABCD with A(0, 0), B(4, 3), C(9, 3) and D(5, 0). What is ABCD, and what is its perimeter?

   • A rhombus with perimeter 20
   • A rectangle with perimeter 20
   • A rhombus with perimeter 28
   • A square with perimeter 20
2. 2.

   Milo's tent has corners A(0, 0), B(8, 0) and C(1, 6). M is the midpoint of AB. How long is the median CM?

   • 3√5
   • √37
   • √85
   • 45
3. 3.

   A(2, y) and B(8, 2) with AB = 10. Esme's points are A(2, y) and B(8, 2), and AB = 10. Which values of y work?

   • y = 10 or y = -6
   • y = 8 or y = -8
   • y = 10 alone
   • y = 12 or y = -8
4. 4.

   Kira's dart board is the circle (x − 2)² + (y + 3)² = 25. A dart lands at P(6, -1). Is P inside, on, or outside the circle?

   • Outside: 20 is greater than the radius 5
   • Inside: 4² + 2² = 20, which is less than 25
   • Outside: (6 − 2)² + (-1 − 3)² = 32 is more than 25
   • Outside: 4 + 2 = 6 is more than the radius 5
5. 5.

   A(1, 3), B(5, -1) and a point P(x, 0) on the x-axis with PA = PB. Tala wants a point P(x, 0) on the x-axis equally far from A(1, 3) and B(5, -1). What is x?

   • -2
   • 2
   • 4
   • 6
6. 6.

   Noah checks A(0, 0), B(3, 4) and C(9, 12). AB = 5, BC = 10 and AC = 15. What do the distances show?

   • They are collinear if and when AB = BC
   • The points are collinear, since AB + BC = AC
   • They form a triangle, since the three distances are different
   • They form a right triangle, since 5 + 10 = 15
7. 7.

   Zee compares two drones measured from the origin: P at (5, -5) and Q at (-7, 2). Which is closer to the origin?

   • P: its distance √50 is less than √53
   • Q: its legs add to 7 + 2 = 9, less than 5 + 5 = 10
   • They are equally far, since 5 and 7 are close
   • Q: -7 + 2 = -5 is smaller than 5 + (-5) = 0
8. 8.

   Ari's hiking route runs from A(-4, 2) to B(6, -4), and M is its midpoint. How long is AM?

   • √68
   • 34
   • √34
   • 2√34
9. 9.

   Ren's tile △ABC has A(0, 0), B(6, 0) and C(0, 8). M is the midpoint of the hypotenuse BC. Which statement about M is true?

   • M is 7 from A and 5 from B and C
   • M is 5 from each of A, B and C
   • M is 25 from each of A, B and C
   • M is 5 from A but 10 from B and C
10. 10.

    Esme's garden has corners A(0, 0), B(5, 0), C(8, 4) and D(0, 4). How long is the fence around it?

    • 20 m
    • 22 m
    • 17 m
    • 24 m