Discussion
Four branches of a company are located at M, N, O and P. M is in the North of N at a distance of 4 km; P is in the South of O at a distance of 2 km; N is in the Southeast of O by 1 km. What is the distance between M and P in km?
Answer: A
The distance is 5.34 km.
Place O at the origin, with east as x and north as y. N is 1 km south-east of O, so N is at \((0.707, -0.707)\). M is 4 km north of N, at \((0.707, 3.293)\). P is 2 km south of O, at \((0, -2)\). Then:
\[ \begin{aligned} MP &= \sqrt{0.707^{2} + 5.293^{2}} \\ &= \sqrt{0.5 + 28.02} \\ &= \sqrt{28.52} \approx 5.34 \end{aligned} \]
28.5 is the value of \(MP^{2}\) before taking the square root.
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