Directions: Use the details below to answer the question.

At a campsite, M is 15 m south of P. K is 8 m west of M. L is 6 m north of K. P is 24 m east of Q, and N is 10 m south of Q.

What is the shortest distance between L and M?

Correct Answer: 10 m

Step-by-Step Explanation:

To find the shortest distance between points L and M, we can analyze their spatial positions based on the given directions.

Step 1: Analyze the relative positions of points K, L, and M.
- We are given that K is 8 m west of M. This means the straight-line segment KM runs along the East-West direction and has a length of 8 m.
- We are also given that L is 6 m north of K. This means the straight-line segment KL runs along the North-South direction and has a length of 6 m.

Step 2: Identify the geometric relationship.
Since the North-South direction is perpendicular to the East-West direction (forming a 90° angle), the line segments KL and KM meet at point K to form a right-angled triangle, ΔLKM, where the angle ∠LKM = 90°.

Step 3: Calculate the shortest distance (LM) using the Pythagorean theorem.
The shortest distance between points L and M is the hypotenuse LM of the right triangle ΔLKM.

According to the Pythagorean theorem:

${\text{LM}}^2={\text{KL}}^2+{\text{KM}}^2$

Substitute the given distances ($\text{KL}=6\text{m}$ and $\text{KM}=8\text{m}$):

${\text{LM}}^2=6^2+8^2$

${\text{LM}}^2=36+64$

${\text{LM}}^2=100$

Taking the square root on both sides:

$\text{LM}=\sqrt{100}=10\text{m}$

Thus, the shortest distance between L and M is 10 m.