Four branches of a company are located at M, N, O and P. M is north of N at a…
2015
Four branches of a company are located at M, N, O and P. M is north of N at a distance of 4 km; P is south of O at a distance of 2 km; N is southeast of O by 1 km. What is the distance between M and P in km?
- A.
5.34
- B.
6.74
- C.
28.5
- D.
45.49
Attempted by 120 students.
Show answer & explanation
Correct answer: A
Approach: place O at (0,0). Let east be the positive x direction and north be the positive y direction.
N is southeast of O by 1 km, so the components are (1/√2, −1/√2). Thus N ≈ (0.7071, −0.7071).
M is 4 km north of N, so add (0,4): M ≈ (0.7071, 3.2929).
P is 2 km south of O, so P = (0, −2).
Vector from P to M: M − P ≈ (0.7071, 5.2929).
Calculation: Δx ≈ 0.7071, Δy ≈ 5.2929, so distance = sqrt((Δx)^2 + (Δy)^2) ≈ sqrt(0.7071^2 + 5.2929^2) ≈ 5.34 km.
Answer: The distance between M and P is approximately 5.34 km.