K is 40 m South-West of L. If M is 40 m South-East of L, then M is in which…

In a direction-sense problem, when two points sit at equal distances from a common reference point along two diagonal directions that mirror each other across the north-south line (here, South-West and South-East), the north-south (vertical) component of both displacements is identical in size. So the two points end up level with each other in the north-south sense, and only their east-west positions differ.

Apply this with East as the positive x-direction and North as the positive y-direction, placing L at the origin.

1. K is 40 m South-West of L, so K's position is 40 m along the South-West diagonal — an equal southward and westward displacement from L.

2. M is 40 m South-East of L, so M's position is 40 m along the South-East diagonal — an equal southward and eastward displacement from L, with the same southward distance as K.

3. Because K and M share the identical southward distance from L, they lie on the same horizontal level; the only difference is that K sits on the west side of that level and M sits on the east side.

4. Moving from K to M therefore involves no north-south shift at all — only a horizontal shift from the west side to the east side.

Confirm with coordinates. Let L = (0, 0), with East as +x and North as +y. Then K = (-40/√2, -40/√2) and M = (40/√2, -40/√2). Subtracting, M − K = (80/√2, 0) — a purely horizontal displacement with zero change in the y-coordinate. A purely positive x-displacement with no y-change is due East, confirming M is due East of K.