Direction: Study the following information to answer the given questions:

Point P is 3m towards south of point Q who is 4m towards east of point R. Point S is 6m towards south of point R while point T is 8m towards west of point S. Point V is 7m towards west of point U who is 3m north of point T.

What is the shortest distance between R and T?

The correct option is 10m.

To find the shortest distance between point R and point T, let us trace the positions of the points step-by-step using standard directional coordinates.

Step 1: Determine the positions of points R, S, and T

1. Point S is 6m towards south of point R. This means point R and point S form a vertical line segment of length 6m, where S is directly below R.
2. Point T is 8m towards west of point S. This means point S and point T form a horizontal line segment of length 8m, where T is to the left of S.

Step 2: Form the right-angled triangle

Points R, S, and T form a right-angled triangle △RST, where the right angle is at point S (∠RST = 90°).

The lengths of the two perpendicular sides are:
- Vertical side, RS = 6m
- Horizontal side, ST = 8m

Step 3: Calculate the shortest distance (Hypotenuse RT)

Using the Pythagoras theorem:

${\mathrm{RT}}^2={\mathrm{RS}}^2+{\mathrm{ST}}^2$

Substitute the given values into the formula:

${\mathrm{RT}}^2=6^2+8^2$

${\mathrm{RT}}^2=36+64$

${\mathrm{RT}}^2=100$

$\mathrm{RT}=\sqrt{100}=10\text{m}$

Thus, the shortest distance between point R and point T is 10m.