Question

The location of Sams house, the library, and the gas station is shown on the map below. What is the distance from Sam’s house to the Gas station?

Answer 1

Sam's house is at a distance of approximately 8.062 meters far from the gas station.

Nota - The statement is incomplete. Complete form is described below:

The location of Sam's house, the library, and the gas station is shown on the map below. What is the distance from Sam's house to gas station? The coordinate of each location are presented below: (Distances are given in miles)

Sam's house

$S(x,y) = (2, -4)$

Library

$L(x,y) = (-5, 2)$

Gas station

$G(x,y) = (3,4)$

The distance ($d$), in miles, is determined by the line segment distance formula, whose vectorial form is presented:

$d = \sqrt{[S(x,y)-G(x,y)]\,\bullet \,[S(x,y)-G(x,y)]}$ (1)

Where $\bullet$ is used in an operation known as dot product.

If we know that $S(x,y) = (2, -4)$ and $G(x,y) = (3,4)$, then the distance between Sam's house and the Gas station is:

$d = \sqrt{(2 - 3)^{2}+[(-4)-4]^{2}}$

$d \approx 8.062\,mi$

Sam's house is at a distance of approximately 8.062 meters far from the gas station.