Study the following information carefully and answer the questions given…

In distance-and-direction problems, every stated direction is a displacement along one of two perpendicular axes: north/south changes the vertical position and east/west changes the horizontal position. To compare two points, add up the individual displacements between them separately along each axis; the sign of the horizontal total decides east or west, the sign of the vertical total decides north or south, and a nonzero result on both axes together gives one of the four diagonal directions (north-east, north-west, south-east, south-west).

1. Fix point M as the origin, (0, 0), taking north and east as the positive vertical and horizontal directions.

2. Point L is 15 m south of M, so L = (0, -15).

3. Point Q is 6 m east of M, so Q = (6, 0).

4. Point R is exactly between M and Q, so R is their midpoint: R = (3, 0).

5. Point S is 6 m south of R, so S = (3, -6).

6. Point T is 7 m east of S, so T = (3 + 7, -6) = (10, -6).

7. Comparing T to M: the horizontal position increases by 10 (east) and the vertical position decreases by 6 (south).

Since T is displaced east of M and south of M at the same time, T lies in the south-east direction from M.

• Horizontal cross-check: the only horizontal moves on the M-to-T path are M→R (+3, east) and S→T (+7, east); R→S contributes no horizontal shift. Adding these independently gives a positive (east) total, matching the coordinate result above.

• Vertical cross-check: the only vertical move on the M-to-T path is R→S (−6, south); M→R and S→T contribute no vertical shift. This confirms a negative (south) total on its own, independent of the coordinate computation.

Both independent checks agree with the coordinate computation, so point T is to the south-east of point M.