Be it known, declared, and set forth on this day: the pupil, age thirteen, hereinafter referred to as "She," received the task of joining five distinct points so as to produce one continuous path composed of consecutive segments whose lengths are √10, √10, 5, and √10, in that sequence, it being expressly noted that no prescribed ordering of the points was supplied.
Whereas She, with due care and mathematical propriety, availed herself of the Pythagorean Theorem ("PT") to compute interpoint distances, matching the numerical squares 10 and 25 as occasion required, and thereby translating geometric restrictions into succinct algebraic checks; and whereas She proceeded to posit coordinates and to place successive segments so that the Euclidean distances conformed to the prescribed magnitudes, the record shall show that such placements were verified by direct substitution and equality of squared lengths.
It is adjudicated and observed (with a certain lightness of manner — a theatrical aside if you will) that She exhibited algorithmic thinking, crisp spatial reasoning, and a methodical approach. The result: a harmonious union of logical rigour and creative flair, duly noted and commended.