A municipal engineer begins inspecting a road pipeline from point A by walking 12\text{ m}… — State PSC Exam

A municipal engineer begins inspecting a road pipeline from point $A$ by walking $12\text{ m}$ towards the East. She then turns to her right and walks $5\text{ m}$ to reach point $B$ . What is the shortest direct distance between point $A$ and point $B$ , and in which direction is point $B$ relative to point $A$ ?

$13\text{ m}$ , South-EastAnswer
B
$17\text{ m}$ , South-East
C
$13\text{ m}$ , North-East
D
$17\text{ m}$ , North-West

Answer

The shortest direct distance between point

A

and point

B

13\text{ m}

, and point

B

lies in the South-East direction relative to point

A

The engineer moves

12\text{ m}

East and then turns right (South) to walk

5\text{ m}

. The straight-line distance forms the hypotenuse of a right triangle with perpendicular sides of

12\text{ m}

and

5\text{ m}

, calculated as

\sqrt{12^2 + 5^2} = 13\text{ m}

. Since point

B

lies to the East and South of point

A

, its position relative to point

A

is South-East.

Step-by-Step Solution

Determine the direction of movement.

Initial movement is

12\text{ m}

East. Turning right while facing East leads to facing South, followed by walking

5\text{ m}

South.

A right turn relative to East points directly South.

Identify the relative cardinal direction of point

B

from point

A

Point

B

is displaced Eastward and Southward from point

A

, placing it in the South-East quadrant relative to point

A

Combining an Eastward vector with a Southward vector results in a South-East displacement.

Calculate the direct straight-line distance using the Pythagorean theorem.

\text{Distance} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13\text{ m}

The perpendicular legs of

12\text{ m}

and

5\text{ m}

form a right-angled triangle where the hypotenuse represents the direct distance.

Key Concept

Direction reorientation and displacement calculation using the Pythagorean theorem

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