Define Coordinate Axes

Let Point Y be at the origin $(0, 0)$. Let North = $+y$, South = $-y$, East = $+x$, West = $-x$.

Trace Each Segment

• Drives 7 km South: $(0, -7)$, facing South • Turns left (East)₁₅ km: $(15, -7)$, facing East • Turns right (South)₃₈ km: $(15, -45)$, facing South • Turns left (East)₁₃ km: $(28, -45)$, facing East • Turns left (North)₃₁ km: $(28, -14)$, facing North • Turns left (West)₂₈ km: $(0, -14)$, facing West • Turns left (South)₁₃ km to Z: $(0, -27)$, facing South

Calculate Return Vector to Point Y

Point Z is at $(0, -27)$ and Point Y is at $(0, 0)$. The vector from Z to Y is $\Delta x = 0$, $\Delta y = 0 - (-27) = +27\text{ km}$. This corresponds to 27 km directly towards North.

$\text{Venu} must drive 27 km towards \text{North} to reach \text{Point} Y.$