A is to the East of B. C is to the South of B. D is to the West of C. In which direction is D with respect to A?
Correct: C
Let Point B be the origin (0,0).
1. A is to the East of B: A = (x, 0) where x > 0 (e.g., A = (5,0)).
2. C is to the South of B: C = (0, -y) where y > 0 (e.g., C = (0,-3)).
3. D is to the West of C: D = (-z, -y) where z > 0 (e.g., D = (-2,-3)).
So, using example values, A = (5,0) and D = (-2,-3).
To find the direction of D with respect to A, we treat A as the new origin.
Relative coordinates of D from A = (D_x - A_x, D_y - A_y) = (-z - x, -y - 0) = (-(z+x), -y).
Since (z+x) is positive (both z and x are positive distances), the x-coordinate of D relative to A is negative, indicating West.
Since y is positive, the y-coordinate of D relative to A is negative, indicating South.
Therefore, point D is in the South-West direction with respect to point A.