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Distance Between Two Points: Classroom Packet

Grade 8 Algebra: Distance Between Two Points

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Whole-number distances

  1. 1. Find the distance between the points:
    (0,0), (3,4)(0, 0),\ (3, 4)
    1122334455667788xy
  2. 2. Find the distance between the points:
    (1,2), (4,6)(1, 2),\ (4, 6)
    1122334455667788xy
  3. 3. Find the distance between the points:
    (0,0), (6,8)(0, 0),\ (6, 8)
    112233445566778899xy
  4. 4. Find the distance between the points:
    (2,1), (7,13)(2, 1),\ (7, 13)
    11223344556677889910101111121213131414xy
  5. 5. Find the distance between the points:
    (−1,−1), (2,3)(-1, -1),\ (2, 3)
    −5−5−4−4−3−3−2−2−1−11122334455xy
  6. 6. Find the distance between the points:
    (0,5), (12,0)(0, 5),\ (12, 0)
    1122334455667788991010111112121313xy
  7. 7. Find the distance between the points:
    (1,1), (1,7)(1, 1),\ (1, 7)
    1122334455667788xy
  8. 8. Find the distance between the points:
    (−3,2), (5,2)(-3, 2),\ (5, 2)
    −5−5−4−4−3−3−2−2−1−1112233445566xy

Answer Key

Level 1

  1. 1. 55
  2. 2. 55
  3. 3. 1010
  4. 4. 1313
  5. 5. 55
  6. 6. 1313
  7. 7. 66
  8. 8. 88

Grade 8 Algebra: Distance Between Two Points

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Negative coordinates and rounding

  1. 1. Find the distance between the points:
    (−2,1), (4,9)(-2, 1),\ (4, 9)
    −5−5−4−4−3−3−2−2−1−11122334455667788991010xy
  2. 2. Find the distance between the points:
    (−3,−4), (5,11)(-3, -4),\ (5, 11)
    −5−5−4−4−3−3−2−2−1−1112233445566778899101011111212xy
  3. 3. Find the distance between the points:
    (1,−2), (4,2)(1, -2),\ (4, 2)
    −5−5−4−4−3−3−2−2−1−11122334455xy
  4. 4. Find the distance between the points:
    (−6,3), (6,−2)(-6, 3),\ (6, -2)
    −7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677xy
  5. 5. Find the distance (nearest tenth):
    (0,0), (1,1)(0, 0),\ (1, 1)
    1122334455667788xy
  6. 6. Find the distance (nearest tenth):
    (1,3), (4,5)(1, 3),\ (4, 5)
    1122334455667788xy
  7. 7. Find the distance (nearest tenth):
    (−2,−1), (3,3)(-2, -1),\ (3, 3)
    −5−5−4−4−3−3−2−2−1−11122334455xy
  8. 8. Find the distance (nearest tenth):
    (2,−3), (−4,1)(2, -3),\ (-4, 1)
    −5−5−4−4−3−3−2−2−1−11122334455xy

Answer Key

Level 2

  1. 1. 1010
  2. 2. 1717
  3. 3. 55
  4. 4. 1313
  5. 5. 2≈1.4\sqrt{2} \approx 1.4
  6. 6. 13≈3.6\sqrt{13} \approx 3.6
  7. 7. 41≈6.4\sqrt{41} \approx 6.4
  8. 8. 213≈7.22\sqrt{13} \approx 7.2

Grade 8 Algebra: Distance Between Two Points

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Simplifying square roots

  1. 1. Find the distance (simplify, then nearest tenth):
    (−1,2), (5,8)(-1, 2),\ (5, 8)
    −5−5−4−4−3−3−2−2−1−1112233445566778899xy
  2. 2. Find the distance (simplify, then nearest tenth):
    (1,0), (6,5)(1, 0),\ (6, 5)
    1122334455667788xy
  3. 3. Find the distance (simplify, then nearest tenth):
    (−3,1), (1,9)(-3, 1),\ (1, 9)
    −5−5−4−4−3−3−2−2−1−11122334455667788991010xy
  4. 4. Find the distance between the points:
    (−6,−2), (6,3)(-6, -2),\ (6, 3)
    −7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677xy
  5. 5. Find the distance between the points:
    (3,−5), (−5,10)(3, -5),\ (-5, 10)
    −6−6−5−5−4−4−3−3−2−2−1−111223344556677889910101111xy
  6. 6. Find the distance between the points:
    (−4,−4), (4,2)(-4, -4),\ (4, 2)
    −5−5−4−4−3−3−2−2−1−11122334455xy
  7. 7. Find the distance between the points:
    (2,2), (−3,−10)(2, 2),\ (-3, -10)
    −11−11−10−10−9−9−8−8−7−7−6−6−5−5−4−4−3−3−2−2−1−11122334455xy
  8. 8. Find the distance between the points:
    (−5,−6), (4,6)(-5, -6),\ (4, 6)
    −7−7−6−6−5−5−4−4−3−3−2−2−1−111223344556677xy

Answer Key

Level 3

  1. 1. 62≈8.56\sqrt{2} \approx 8.5
  2. 2. 52≈7.15\sqrt{2} \approx 7.1
  3. 3. 45≈8.94\sqrt{5} \approx 8.9
  4. 4. 1313
  5. 5. 1717
  6. 6. 1010
  7. 7. 1313
  8. 8. 1515