Discussion
Consider the following information: A person starts from point 'O'
| Row | Movement Pattern | How far from O | Final Direction from start |
|---|---|---|---|
| 1 | 4 m East → 3 m South | 7 m | East |
| 2. | 8 m North → 15 m West | 17 m | North-West |
| 3. | 6 m South → 8 m East | 10 m | West |
In how many of the above rows is/are the given information correctly matched?
Answer: A
Only one row is correctly matched.
Each pair of perpendicular moves forms a right triangle, so the distance from O is the hypotenuse.
\[ \begin{aligned} \text{Row 1} &: \sqrt{4^2 + 3^2} = 5 \text{ m, South-East} \\ \text{Row 2} &: \sqrt{8^2 + 15^2} = 17 \text{ m, North-West} \\ \text{Row 3} &: \sqrt{6^2 + 8^2} = 10 \text{ m, South-East} \end{aligned} \]
Row 2 is fully right. Row 1 adds the legs (7 m) instead of using Pythagoras and gives East instead of South-East. Row 3 has the distance right but the direction wrong: 6 m South then 8 m East leaves the person South-East of O, not West.
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