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?

Theo Correct answer is Option 1. 

Key Points

Given Information:

⇒ M is in the North of N by 4 km.

This means if N is at (x, y), then M is at (x, y + 4).

⇒ P is in the South of O by 2 km.

This means if O is at (a, b), then P is at (a, b - 2).

⇒ N is in the Southeast of O by 1 km.

This means N is 1 km diagonally from O.

⇒ In a 45-degree southeast direction, the movement in both x and y directions is by  1/ \(sqrt[2]\) ≈0.707 km.

So, if O is at (a, b), then N is at (a + 0.707, b - 0.707).

Assign coordinates:

⇒ O = (0,0)

⇒  N = (0.707, -0.707) (1 km Southeast of O)

⇒  M = (0.707, 3.293) (4 km North of N)

⇒  P = (0, -2) (2 km South of O)

Use distance formula:

⇒ d = \(sqrt((x2 - x1)^2 + (y2 - y1)^2)\)

Applying values:

⇒  d =\( sqrt((0.707 - 0)^2 + (3.293 - (-2))^2)\)

Simplifying:

⇒ d = \(sqrt(0.5 + 27.34) = sqrt(27.84)\) ≈ 5.34 km

Hence  The closest answer is 5.34, so the correct choice is: