In which direction is point V with respect to point R? Study the following information carefully and answer the questions given below:
Riya starts walking from point Z towards west for 11m to reach point Y. Then, she turns right and walks for 4m to reach point X. Then she again turns right and walks for 14m to reach point W and then finally she turns towards south and walks for 6m to reach point V.
Karan starts walking towards north for 2m from point Z to reach at point U. Then, he takes right and left turn and walks for 6m and 9m to reach point T and S respectively. Then, he takes left turn and walks for 5m to reach point R. -

The correct option is South-east.

Let us track the paths taken by Riya and Karan step-by-step on a standard 2D Cartesian coordinate plane, where the positive x-axis represents East, negative x-axis represents West, positive y-axis represents North, and negative y-axis represents South.

Let the starting point Z be at the origin (0, 0).

1. Riya's Movement:
• Riya starts at point Z(0, 0) and walks 11 m towards West to reach point Y.
Coordinates of Y = (-11, 0).
• From Y(-11, 0), she turns right (towards North) and walks 4 m to reach point X.
Coordinates of X = (-11, 0 + 4) = (-11, 4).
• From X(-11, 4), she turns right (towards East) and walks 14 m to reach point W.
Coordinates of W = (-11 + 14, 4) = (3, 4).
• From W(3, 4), she turns South and walks 6 m to reach point V.
Coordinates of V = (3, 4 - 6) = (3, -2).

2. Karan's Movement:
• Karan starts at point Z(0, 0) and walks 2 m North to reach point U.
Coordinates of U = (0, 2).
• From U(0, 2), he turns right (towards East) and walks 6 m to reach point T.
Coordinates of T = (0 + 6, 2) = (6, 2).
• From T(6, 2), he turns left (towards North) and walks 9 m to reach point S.
Coordinates of S = (6, 2 + 9) = (6, 11).
• From S(6, 11), he turns left (towards West) and walks 5 m to reach point R.
Coordinates of R = (6 - 5, 11) = (1, 11).

3. Determining the Direction of Point V with Respect to Point R:
• Coordinates of R = (1, 11)
• Coordinates of V = (3, -2)

Comparing the coordinates of V with respect to R:
• The x-coordinate of V (3) is greater than the x-coordinate of R (1), which means V is to the East of R.
• The y-coordinate of V (-2) is less than the y-coordinate of R (11), which means V is to the South of R.

Combining these two directions, point V is in the South-east direction with respect to point R.