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A family is planning a vacation in which to travel from their home in Oregon to the home of relatives who live in North Carolina. The coordinates as their home on a map were (116,27), and the coordinates of the relative's home on the map are (33, 51). If each map coordinate represents 55 kilometers, what is the distance between the two homes to the nearest mile?​

Answer :

Considering the distance between the two points and the scale, the distance between the two homes is of 2,953 miles.

What is the distance between two points?

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In this problem, the points are:

(116, 27) and (33,51).

Hence the distance between them is:

[tex]D = \sqrt{(116 - 33)^2+(27 - 51)^2}[/tex]

D = 86.4.

Each unit represents 55 kilometers, hence the distance in km is:

D = 86.4 x 55 = 4752 km.

Each km represents 0.621371 miles, hence the distance in miles is:

4752 x 0.621371 = 2,953 miles.

More can be learned about the distance between two points at https://brainly.com/question/18345417

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