← Back to the Distance Formula worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 8.G.B.8 · Level: Grade 8
Problem 1 Across a row
The y-coordinates match, so subtract the x-coordinates: |5 − (−7)| = 12.
The distance is 12 units.
Problem 2 Down a column
The x-coordinates match: |9 − (−6)| = 15.
The distance is 15 units.
Problem 3 From the origin
d = √(36² + 77²) = √(1,296 + 5,929) = √7,225 = 85.
The distance is 85 units.
Problem 4 Not a whole number
Legs: 2 − (−4) = 6 and −2 − 7 = −9, so the vertical leg is 9.
d = √(36 + 81) = √117 ≈ 10.82.
The distance is about 10.8 units.
Problem 5 Read the graph
K(−3, 5) and L(4, −3). Horizontal leg: 7. Vertical leg: 8.
d = √(49 + 64) = √113 ≈ 10.63.
√113 ≈ 10.6 units
Problem 6 Twenty units
Legs: 10 − (−6) = 16 and 9 − (−3) = 12.
d = √(256 + 144) = √400 = 20.
20 units
Problem 7 Equal legs
Legs: |−4 − 2| = 6 and |−1 − (−7)| = 6.
d = √(36 + 36) = √72 = 6√2 ≈ 8.49.
6√2 ≈ 8.5 units
Problem 8 Right triangle on a grid
AB² = 3² + 1² = 10. BC² = 1² + 3² = 10. AC² = 2² + 4² = 20.
AB² + BC² = 10 + 10 = 20 = AC².
Yes, it is a right triangle with the right angle at B
Problem 9 Perimeter of a rectangle
Width: 4 − (−2) = 6. Height: 2 − (−3) = 5.
Perimeter: 2(6 + 5) = 22.
22 units
Problem 10 Perimeter of a triangle
Horizontal side: 5. Vertical side: 12. Slanted side: √(25 + 144) = √169 = 13.
Perimeter: 5 + 12 + 13 = 30.
30 units
Problem 11 Triangle perimeter from a graph
DE = 6 and EF = 5 by counting. DF = √(6² + 5²) = √61 ≈ 7.81.
Perimeter: 6 + 5 + 7.81 = 18.81.
About 18.8 units
Problem 12 Find the missing coordinate
(x − 2)² + (9 − 1)² = 10², so (x − 2)² + 64 = 100.
(x − 2)² = 36, so x − 2 = 6 or x − 2 = −6.
x = 8 or x = −4
Problem 13 Isosceles check
AB = 6. AC = √(3² + 6²) = √45. BC = √(3² + 6²) = √45.
AC = BC, so the triangle is isosceles.
Perimeter: 6 + 2√45 = 6 + 13.42 = 19.42.
Isosceles; perimeter ≈ 19.4 units
Problem 14 Trapezoid perimeter
AB = 4 (horizontal). DA = 4 (vertical). CD = 7 (horizontal).
BC = √((4 − 1)² + (2 − (−2))²) = √(9 + 16) = 5.
Perimeter: 4 + 5 + 7 + 4 = 20.
20 units
Problem 15 Which is closer?
OA² = 49 + 25 = 74. OB² = 36 + 36 = 72.
Since 72 is less than 74, B is closer (√72 ≈ 8.49 compared with √74 ≈ 8.60).
Point B is closer
Problem 16 Hiking map
Legs: 3 − (−5) = 8 and 2 − (−3) = 5.
d = √(64 + 25) = √89 ≈ 9.43.
About 9.4 miles
Problem 17 Drone delivery
Legs: 9 − (−6) = 15 and 6 − (−2) = 8.
d = √(225 + 64) = √289 = 17 units.
17 · 0.25 = 4.25.
4.25 miles
Problem 18 Garden fence
Sides in units: 8, 15, and √(64 + 225) = 17. Perimeter: 8 + 15 + 17 = 40 units.
40 · 2 = 80 feet, and 80 · $3.50 = $280.
$280
Problem 19 Robot route
AB = √(3² + 6²) = √45 ≈ 6.71. BC = √(6² + 6²) = √72 ≈ 8.49.
Route: 6.71 + 8.49 = 15.19. Straight path AC = 4 − (−5) = 9.
Savings: 15.19 − 9 = 6.19.
Route ≈ 15.2 units; the straight path is about 6.2 units shorter
Problem 20 Rhombus on the grid
WX = √(5² + 2²) = √29. XY = √(5² + 2²) = √29. YZ = √(5² + 2²) = √29. ZW = √(5² + 2²) = √29.
All sides equal √29 ≈ 5.385.
Perimeter: 4√29 ≈ 21.54.
All sides are √29; perimeter ≈ 21.5 units