Question 6185: Endpoint, Net Displacement, and Step Magnitude

Original question and givens

Integer start=-3, signed steps s1=10, s2=-5. Give (endpoint, s1+s2, |s1|+|s2|).

• G001 — Integer start=-3, signed steps s1=10, s2=-5. Give (endpoint, s1+s2, |s1|+|s2|).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-integer

Step-by-step derivation

declared exact integer or rational-representation protocol

retain signs,ordered operands and original index order

signed net displacement := sum(10, -5)

signed net displacement = 5

final position := sum(-3, 5)

final position = 2

steps=(10,-5)

absolute step lengths=(10,5)

sum of step lengths := sum(10, 5)

sum of step lengths = 15

Reverse checks

• S005 · premise_and_result_audit — Recompute sum of step lengths with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S003 · premise_and_result_audit — Recompute final position with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute signed net displacement with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(2, 5, 15)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.