Question

On a city map where each unit represents one mile, two cell phone towers are located at N(2,8) and P(17,5). To the nearest whole mile, how far apart are the two cell phone towers?

Answer 1

Answer: 15 miles.

Explanation:

You need to use the formula for calculate the distance between two points. This is:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Given the points N(2,8) and P(17,5), you know that:

`x_2=17\\x_1=2\\y_2=5\\y_1=8`

Then, substituting values into the formula, you get:

`d_((NP))=√((17-2)^2+(5-8)^2)\\\\d_((NP))=15.29\ miles`

To the nearest whole mile, this is:

`d_((NP))=15 \ miles`

Answer 2

For this case we must find the distance between two points:

By definition we have to:

`d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}`

We have as data that:

`(x_ {1}, y_ {1}) :( 2,8)\\(x_ {2}, y_ {2}) :( 17,5)`

Substituting:

`d = \sqrt {(17-2) ^ 2 + (5-8) ^ 2}\\d = \sqrt {(15) ^ 2 + (- 3) ^ 2}\\d = \sqrt {225 + 9}\\d = \sqrt {234}\\d = 15.30`

Round and we have that the distance is 15 miles

ANswer:

15 miles