The distance formula

Grade 10 Math Worksheet

Circle the best answer.

1. 1.

   Luz's sled path △ABC has A(1, 1), B(7, 1) and C(4, 5). Luz classifies it by its sides. Which is correct?

   • Equilateral, since each side is about 5 or 6
   • Isosceles: AC = BC = 5 and AB = 6
   • Scalene, since the three slopes are different
   • Right, since AC = BC
2. 2.

   Bo's sail has corners P(-1, 2), Q(3, 6) and R(7, 2). Is △PQR a right triangle?

   • Yes: PQ² + QR² = 32 + 32 = 64 = PR², so the right angle is at Q
   • No: PQ and QR are not whole numbers, so there is no right angle
   • Yes: PQ + QR is greater than PR
   • No: 4√2 + 4√2 = 8√2, which is not 8
3. 3.

   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 28
   • A square with perimeter 20
   • A rectangle with perimeter 20
   • A rhombus with perimeter 20
4. 4.

   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
   • 45
   • √85
   • √37
5. 5.

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

   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: 4 + 2 = 6 is more than the radius 5
   • Outside: (6 − 2)² + (-1 − 3)² = 32 is more than 25
7. 7.

   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
   • 4
   • -2
   • 6
8. 8.

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

   • The points are collinear, since AB + BC = AC
   • They form a right triangle, since 5 + 10 = 15
   • They form a triangle, since the three distances are different
   • They are collinear if and when AB = BC
9. 9.

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

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