Kamal starts from Point A and drives 17 km towards south. He t... | Mathematics MCQ | Examoogle

MathematicsPrevious Year Paper 2024

Kamal starts from Point A and drives 17 km towards south. He then takes a left turn, drives 13 km, turns left and drives 21 km. He then takes a left turn and drives 18 km. He takes a final left turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90° turns only unless specified.)

3 km to the east

5 km to the east

4 km to the east

6 km to the east

Correct Answer

📐 MA • Math Coordinate GeometryMathematicsPrevious Year Paper 2024

Option B

5 km to the east

Quick Summary:

Track net displacements along North-South and East-West axes independently. Net NS movement = +17 - 21 + 4 = 0 km. Net EW movement = -13 - 18 = -31 km from start? Let's check step-by-step.

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📐MAMath SolutionCoordinate Geometry

📋 Given

Starting point A = (0, 21), moves 17 km South, 13 km West, 21 km North, 18 km West, and 4 km South to Point P.

🔢 Formula Used

d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​

⚡ Exam Hall Shortcut / Speed Trick

Track net displacements along North-South and East-West axes independently. Net NS movement = +17 - 21 + 4 = 0 km. Net EW movement = -13 - 18 = -31 km from start? Let's check step-by-step.

⚠️ Common Student Trap / Pitfall

Confusing left and right turns relative to the current heading, or miscalculating the net coordinates relative to Point A.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Step 1: Set up Coordinate System

Let Point A be the origin $(0, 0)$ on a Cartesian plane where North is $+y$ , South is $-y$ , East is $+x$ , and West is $-x$ .

A=(0,0)A = (0, 0)A=(0,0)r

Step 2: Trace Movements

From $A(0,0)$ , drives $17\text{ km}$ South $\to (0, -17)$ .
Left turn (faces East), drives $13\text{ km} \to (13, -17)$ .
Left turn (faces North), drives $21\text{ km} \to (13, 4)$ .
Left turn (faces West), drives $18\text{ km} \to (13 - 18, 4) = (-5, 4)$ .
Final left turn (faces South), drives $4\text{ km} \to (-5, 4 - 4) = (-5, 0)$ [Point P].

P=(−5,0)P = (-5, 0)P=(−5,0)r

Step 3: Calculate Distance and Direction to A

Point P is at $(-5, 0)$ and Point A is at $(0, 0)$ . To reach A from P, Kamal needs to move $5\text{ km}$ along the positive x-axis, which corresponds to the East direction.

Distance=5 km,Direction=East\text{Distance} = 5\text{ km}, \text{Direction} = \text{East}Distance=5 km,Direction=East

✅

Option B is correct because Kamal ends up at Point P, which is 5 km west of Point A, meaning he must travel 5 km to the east to reach Point A again.

Core Concepts Used

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Coordinate Geometry Direction Sense Test Displacement Vector

💡 EXAM TIP

Direction problems can always be modeled as vector addition or coordinate movements to avoid visual errors.

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