Directions (79-81): Answer the questions based on the information given below.

Seven delivery agents P, Q, R, S, T, U, and V are parked at different spots in a logistics hub. S is 14m west of T, who is 10m west of V. R is east of S. The distance between V and S is twice the distance between R and S. U is 16m north of R. P is 12m east of U. P is 10m north of Q.

In which direction is P with respect to V?

The correct option is North.

To determine the direction of agent P with respect to agent V, we can map out the positions of all delivery agents step-by-step using a Cartesian coordinate system, where V is taken as the reference origin $(0,0)$.

Step 1: Locate T and S relative to V
• V is located at $(0,0)$.
• T is 10m west of V, so the position of T is $(-10,0)$.
• S is 14m west of T, so the position of S is:

$\text{Position of S}=(-10-14,0)=(-24,0)$
• Thus, the total distance between V and S is 24m.

Step 2: Locate R relative to S
• The distance between V and S is twice the distance between R and S:

$\text{Distance between R and S}=\frac{24}{2}=12\text{m}$
• Since R is east of S, we add 12m to the x-coordinate of S:

$\text{Position of R}=(-24+12,0)=(-12,0)$

Step 3: Locate U relative to R
• U is 16m north of R, so we add 16m to the y-coordinate of R:

$\text{Position of U}=(-12,0+16)=(-12,16)$

Step 4: Locate P relative to U
• P is 12m east of U, so we add 12m to the x-coordinate of U:

$\text{Position of P}=(-12+12,16)=(0,16)$

Step 5: Determine the direction of P with respect to V
• V is at coordinates $(0,0)$.
• P is at coordinates $(0,16)$.
• Since both positions have the same x-coordinate ($x=0$) and P has a positive y-coordinate, agent P is located directly to the North of agent V at a distance of 16m.