QB_PH_GA_030: Analytical & Spatial Aptitude

A person walks $10\text{ meters}$ North, turns right and walks $15\text{ meters}$, then turns right again and walks $10\text{ meters}$. How far (in meters) is the person now from their original starting point?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Cartesian Coordinate Representation** (Starting at $(0, 0)$): - Step 1 (10 m North): Moves along $+y$ axis to $(0, 10)$. - Step 2 (Turn right $\implies$ East, 15 m): Moves along $+x$ axis to $(15, 10)$. - Step 3 (Turn right $\implies$ South, 10 m): Moves along $-y$ axis to $(15, 10 - 10) = (15, 0)$. 2. **Euclidean Distance from Origin**: $d = \sqrt{(x - x_0)^2 + (y - y_0)^2} = \sqrt{(15 - 0)^2 + (0 - 0)^2} = 15\text{ m}$ 3. **Official Answer**: 15 meters.