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 U with respect to T?

Correct Answer: North-west

Let us analyze the given statements step-by-step to find the relative positions of the delivery agents on a standard coordinate plane, where East-West corresponds to the horizontal axis and North-South corresponds to the vertical axis.

Step 1: Determine positions of S, T, and V along the East-West line
- Agent S is 14 m west of agent T.
- Agent T is 10 m west of agent V.
Taking the position of S as the origin point (0, 0):
- Position of S = (0, 0)
- Position of T = 14 m East of S = (14, 0)
- Position of V = 10 m East of T = 14 + 10 = (24, 0)

Step 2: Determine the position of agent R
- The total distance between V and S is:
$\text{Distance(V, S)}=24\text{m}$
- We are given that the distance between V and S is twice the distance between R and S:
$\text{Distance(R, S)}=\frac{\text{Distance(V, S)}}{2}=\frac{24}{2}=12\text{m}$
- Since R is to the east of S, agent R is located 12 m east of S along the horizontal axis.
Position of R = (12, 0)

Step 3: Determine the position of agent U
- Agent U is 16 m north of R.
Starting from R at (12, 0) and moving 16 m north along the vertical axis:
Position of U = (12, 16)

Step 4: Find the direction of U with respect to T
- Position of T = (14, 0)
- Position of U = (12, 16)
Comparing the coordinates of U relative to T:
- Horizontal component: U is at x = 12 m while T is at x = 14 m (12 < 14), so U is 2 m West of T.
- Vertical component: U is at y = 16 m while T is at y = 0 m (16 > 0), so U is 16 m North of T.

Combining the horizontal (West) and vertical (North) directions, agent U is in the North-west direction with respect to T.