Question

Shivang visits his village after a long time. He goes 7 km north from the Domino’s outlet. He then takes a right turn and walks for 14 km to reach a temple. The village bus stop is 14 km east of the Domino’s outlet. There is a mall in the village that is 10 km south of the bus stop. There is a park exactly in between the mall and the bus stop. What exactly is the location of this park in comparison with the temple?

• A. 10 km south
• B. 12 km south
• C. 12 km north
• D. 10 km north

Hint:

In direction problems, fix one point as the origin and use coordinate geometry to avoid confusion and errors.

Answer 1

The Correct Option is B

Step 1: Fix the Domino’s outlet as the reference point.
Assume the Domino’s outlet is at point \( O(0,0) \).
Step 2: Find the location of the temple.
Shivang goes 7 km north from Domino’s outlet, reaching point \( (0,7) \).
From there, he takes a right turn (east) and walks 14 km to reach the temple.
So, the temple is located at \( (14,7) \).
Step 3: Find the location of the bus stop.
The bus stop is 14 km east of the Domino’s outlet.
So, the bus stop is at \( (14,0) \).
Step 4: Find the location of the mall.
The mall is 10 km south of the bus stop.
So, the mall is at \( (14,-10) \).
Step 5: Find the location of the park.
The park is exactly midway between the bus stop \( (14,0) \) and the mall \( (14,-10) \).
Midpoint coordinates:
\[ \left(14,\frac{0 + (-10)}{2}\right) = (14,-5) \]
Step 6: Compare the park’s location with the temple.
Temple is at \( (14,7) \).
Park is at \( (14,-5) \).
Vertical distance between them:
\[ 7 - (-5) = 12 \text{ km} \]
Since the park lies below the temple, it is 12 km south of the temple.
Step 7: Conclusion.
The park is located 12 km south of the temple.