Point K is located 40 m to the South-West of point L. Point M is located 40 m to the South-East of point L. With respect to point K, in which direction does point M lie?

Introduction:
This direction–sense question involves three points placed at fixed distances and directions: K, L and M. We are told where K and M lie relative to L, and we must determine the direction of M with respect to K. The displacements are along diagonals (South-West and South-East), so a simple coordinate approach helps clarify their relative positions.

Given Data / Assumptions:
• K is 40 m to the South-West of L.• M is 40 m to the South-East of L.• South-West means equally towards the South and West from L; South-East similarly means equally towards the South and East.• We are asked: In which direction is M from K?

Concept / Approach:
We place L at the origin of a coordinate system. South is taken as negative y, North as positive y, East as positive x and West as negative x. Moving South-West from L moves us some equal distance in the negative x and negative y directions. Moving South-East from L moves us the same distance in positive x and negative y. Since the magnitudes are equal (40 m in each diagonal case), we can reason with equal components without worrying about the exact trigonometric values.

Step-by-Step Solution:
Step 1: Place L at coordinates (0, 0).Step 2: A 40 m move towards South-West from L can be represented as going some distance “a” units west (negative x) and the same distance “a” units south (negative y). Thus, K can be represented approximately as (−a, −a).Step 3: Similarly, a 40 m move towards South-East from L can be represented as going “a” units east (positive x) and “a” units south (negative y). Thus, M is at (a, −a).Step 4: To find the direction of M from K, compute the displacement from K to M. This displacement vector is (a − (−a), −a − (−a)) = (2a, 0).Step 5: A displacement of (2a, 0) has a positive x-component and zero y-component, which means it is purely towards the East.Step 6: Therefore, M lies due East of K.

Verification / Alternative check:
You can also visualize L at the top of an isosceles triangle, with K and M forming the base corners at equal distances downwards. The base of that triangle is horizontal. From the left base point (K) you move horizontally to the right to reach the right base point (M). A horizontal move from left to right corresponds directly to the East direction.

Why Other Options Are Wrong:
West would correspond to moving from right to left, which is the direction of K from M, not M from K. South would require a downward displacement, which does not happen when going from K to M. North-East would involve both an upward and rightward movement, whereas there is no vertical change between K and M. South-East also has a downward component, but here the y-coordinates are equal, so that option is not appropriate.

Common Pitfalls:
Candidates often confuse the phrase "direction of M from K" with "direction of K from M". Direction questions are not symmetric: East of K means West of M. Another common error is to focus only on the words South-West and South-East and incorrectly pick South, without carefully computing the relative position. A quick sketch of the three points usually makes the situation clear.

Final Answer:
With respect to K, point M lies directly to the East.