Distance Formula Test Answer Key with Scoring – Grade 8

Question 1 Grid-line distances (2 points)

(a) |4 − (−9)| = 13 units

(b) |6 − (−8)| = 14 units

Scoring: 1 point per part.

Question 2 Distance from a graph (3 points)

(a) Horizontal: |5 − (−2)| = 7. Vertical: |2 − (−3)| = 5. 7 and 5

(b) AB = √(49 + 25) = √74

(c) √74 ≈ 8.60, so 8.6

Scoring: 1 point per part.

Question 3 Two distances (3 points)

(a) Legs: |−6 − 1| = 7 and |3 − (−5)| = 8. √(49 + 64) = √113 ≈ 10.6

(b) √(144 + 1,225) = √1,369 = 37

Scoring: part (a) 1 point for the legs, 1 point for the distance; part (b) 1 point.

Question 4 Right triangle test (3 points)

(a) AB² = 6² + 2² = 40. BC² = 2² + 6² = 40. AC² = 4² + 8² = 80.

(b) 40 + 40 = 80, so AB² + BC² = AC². Yes, a right triangle with the right angle at B

Scoring: part (a) 2 points for all three values (1 point if two are correct); part (b) 1 point for the converse reasoning.

Question 5 Perimeter on a grid (3 points)

(a) AB = 8, CD = |2 − (−4)| = 6, DA = 5, BC = √((4 − 2)² + (−2 − 3)²) = √29 ≈ 5.39.

(b) 8 + 5.39 + 6 + 5 = 24.39.

About 24.4 units

Scoring: part (a) 1 point for the three grid-line sides, 1 point for BC; part (b) 1 point.

Question 6 Missing coordinate (2 points)

(6 − (−2))² + (y − 3)² = 17², so 64 + (y − 3)² = 289.

(y − 3)² = 225, so y − 3 = 15 or −15. Since y is positive, y = 18.

y = 18

Scoring: 1 point for the equation, 1 point for the value of y.

Question 7 Drone flight (2 points)

Legs: 8 − (−4) = 12 and 4 − (−1) = 5.

d = √(144 + 25) = 13 units, and 13 · 0.2 = 2.6.

2.6 miles

Scoring: 1 point for the distance in units, 1 point for the conversion.

Question 8 Robot path (2 points)

AB = √(6² + 6²) = √72 ≈ 8.49. BC = |3 − (−4)| = 7.

Total: 8.49 + 7 = 15.49.

About 15.5 units

Scoring: 1 point for each leg of the route.