A delivery cyclist starts from a warehouse and rides 12\text{ km} towards the South. He th… — State PSC Exam

A delivery cyclist starts from a warehouse and rides $12\text{ km}$ towards the South. He then turns left and rides $9\text{ km}$ . What is the shortest direct distance, in kilometers, between his current location and the warehouse?

Answer: 15 km

Answer

The shortest direct distance between the current location and the warehouse is

15\text{ km}

The straight-line displacement forms the hypotenuse of a right triangle with perpendicular sides of length

12\text{ km}

and

9\text{ km}

. Applying the Pythagorean theorem yields

\sqrt{12^2 + 9^2} = \sqrt{225} = 15\text{ km}

Step-by-Step Solution

Determine the cardinal directions of each movement segment

First displacement is

12\text{ km}

South. Turning left while facing South directs the cyclist towards East, so the second displacement is

9\text{ km}

East.

A 90-degree left turn from South points towards East.

Set up the right-angled displacement triangle

The two perpendicular legs of the right triangle are

12\text{ km}

(South) and

9\text{ km}

(East).

South and East form a perpendicular angle (

90^\circ

Calculate the straight-line distance using the Pythagorean theorem

Distance

= \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15\text{ km}

The direct distance corresponds to the hypotenuse:

c = \sqrt{a^2 + b^2}

Key Concept

Shortest direct distance calculation using the Pythagorean theorem

Estimated Time:45s

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