Worked example · Computer Science · Year 7 · Beginner
LNF: Numeracy → Using geometry skills → Position · DCF: Problem-solving and modelling
A complete model response and answer key for the cover teacher and for marking. Headline answers: Step 1 fixed commands: Command 4 = LINE_TO (5, 8), Command 6 = LINE_TO (7, 10), Command 10 = LINE_TO (11, 10). Step 2 measurements: base width = 10 units, wall height = 8 units, outer rectangle perimeter = 36 units, full castle tower perimeter = 44 units. Step 3 shield script: MOVE_TO (5, 7), LINE_TO (11, 7), LINE_TO (11, 5), LINE_TO (8, 3), LINE_TO (5, 5), LINE_TO (5, 7).
| Command no. | Buggy command in file | What mistake was made? | Corrected command |
|---|---|---|---|
| Command 4 | LINE_TO (5, 9) |
The y-coordinate was 9 instead of 8, so the left-hand gap only went down 1 unit instead of 2 units and made the gap sloping. | LINE_TO (5, 8) |
| Command 6 | LINE_TO (10, 7) |
The x and y coordinates were swapped (plotted up first, across second). It went to (10, 7) instead of the top-left of the middle merlon at (7, 10). |
LINE_TO (7, 10) |
| Command 10 | LINE_TO (11, 11) |
The y-coordinate was 11 instead of 10, making the right-hand merlon spike 1 unit higher than the top of the tower. | LINE_TO (11, 10) |
(b) Completed Grid A (showing both the corrected castle tower and the Step 3 shield):
Identifies all three coordinate errors (wrong vertical depth, transposed x and y coordinates, and wrong vertical height) and plots the symmetrical shape accurately. Evidences criteria 1 and 2.
| Measurement | Calculation using coordinates | Answer (grid units) |
|---|---|---|
(a) Width of tower base from (3, 2) to (13, 2) |
13 − 3 = 10 | 10 units |
(b) Height of left wall from (3, 2) to (3, 10) |
10 − 2 = 8 | 8 units |
(c) Perimeter of simple outer rectangle (3, 2), (3, 10), (13, 10), (13, 2) |
10 + 8 + 10 + 8 | 36 units |
| (d) Full perimeter of the castle tower (including the four 2-unit vertical steps in the battlements) | Base (10) + left wall (8) + right wall (8) + 5 horizontal top pieces (2 + 2 + 2 + 2 + 2 = 10) + 4 vertical steps in gaps (2 + 2 + 2 + 2 = 8) = 36 + 8 | 44 units |
Uses coordinate subtraction to find horizontal and vertical lengths and accounts for the four 2-unit vertical steps inside the battlements when finding the full perimeter. Evidences criterion 3.
| Step | What the virtual pen does | Vector command |
|---|---|---|
| 1 | Move pen to top-left corner A without drawing | MOVE_TO (5, 7) |
| 2 | Draw top horizontal edge across to top-right corner B | LINE_TO (11, 7) |
| 3 | Draw right vertical edge down to right shoulder C | LINE_TO (11, 5) |
| 4 | Draw sloping edge down to the bottom point D on the mirror line | LINE_TO (8, 3) |
| 5 | Draw sloping edge up to left shoulder E | LINE_TO (5, 5) |
| 6 | Draw left vertical edge back up to A to close the shield | LINE_TO (5, 7) |
Starts with MOVE_TO, uses LINE_TO for each edge in clockwise order, and returns to (5, 7) to close the polygon. Evidences criterion 4.
A vector graphic stores the badge as mathematical coordinates and line instructions rather than fixed pixels, so when it is enlarged onto a 3-metre sports hall banner the computer recalculates the lines and keeps every edge completely sharp. A pixel (bitmap) image would stretch its fixed squares and look blocky and blurred. To double the size of the badge from (0, 0), the computer multiplies every x-coordinate and every y-coordinate by 2.
Explains why vector graphics scale without losing quality and links scaling to multiplying coordinates by a scale factor. Evidences criterion 4.
(10, 14), B = (22, 14), C = (22, 10), D = (16, 6), E = (10, 10), and back to A = (10, 14).MOVE_TO (8, 10), 2: LINE_TO (8, 12), 3: LINE_TO (10, 11), 4: LINE_TO (8, 11).(10, 7) vs (7, 10) transposition bug using the line of symmetry x = 8.MOVE_TO) and drawing an edge (LINE_TO), and closes the polygon.