Listen up — I expect complete, neat work. Show the arithmetic; do not guess.
We are given five marked grid points on a 7×7 grid: A = (6,2), B = (6,3), C = (5,0), D = (1,3), E = (3,2). We must form a single continuous path that visits each point exactly once so that the four consecutive segment lengths equal, in order, 1, √10, 5, √5.
Step 1 — Use the Pythagorean theorem to compute distances between promising pairs. For two points (x1,y1) and (x2,y2) the distance is sqrt((x2−x1)^2 + (y2−y1)^2). I will compute only the distances we need to test the sequence; compute carefully and write them down on your paper.
Distance AB: A(6,2) → B(6,3) dx = 6−6 = 0, dy = 3−2 = 1 distance^2 = 0^2 + 1^2 = 1 => distance = 1 Distance BC: B(6,3) → C(5,0) dx = 5−6 = −1, dy = 0−3 = −3 distance^2 = (−1)^2 + (−3)^2 = 1 + 9 = 10 => distance = √10 Distance CD: C(5,0) → D(1,3) dx = 1−5 = −4, dy = 3−0 = 3 distance^2 = (−4)^2 + 3^2 = 16 + 9 = 25 => distance = 5 Distance DE: D(1,3) → E(3,2) dx = 3−1 = 2, dy = 2−3 = −1 distance^2 = 2^2 + (−1)^2 = 4 + 1 = 5 => distance = √5
Step 2 — Put the pieces together. The distances we computed give the exact required sequence if we follow the order:
- A(6,2) → B(6,3) has length 1
- B(6,3) → C(5,0) has length √10
- C(5,0) → D(1,3) has length 5
- D(1,3) → E(3,2) has length √5
Therefore the correct continuous path that visits every given dot once and matches the distances in the given order is:
(6,2) → (6,3) → (5,0) → (1,3) → (3,2)
Step 3 — Draw it on the 7×7 grid. Start at (6,2), draw a short vertical segment up to (6,3). From (6,3) draw a diagonal down-left to (5,0). From (5,0) draw a long diagonal up-left to (1,3). Finish with a small diagonal down-right to (3,2). Label each segment with its length (1, √10, 5, √5) — neatness matters.
Marking checklist (exemplary submission, ACARA v9 aligned):
- All five points listed and labelled.
- Distance calculations shown for each used segment (dx, dy, squared sum, square root).
- Correct order of points and matching segment lengths: (6,2) → (6,3) → (5,0) → (1,3) → (3,2).
- Clear final diagram on the 7×7 grid with segment lengths annotated.
Do not hand me a guess. Work exactly as above and you will earn full marks. If anything is unclear, write the computations exactly as in the pre block and I will check your arithmetic.