Question

What is the distance between `(-15,36)` and # (–3, 2) #?

Answer 1

The distance is `10sqrt13` or about `36.056` (rounded to nearest thousandth's place).

Explanation:

The formula for the distance of 2-dimensional coordinates is: `d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)`

We have the two coordinates, so we can plug in the values for `x` and `y`:
`d = sqrt((-3-(-15))^2 + (2-36)^2)`

Now we simplify:
`d = sqrt((12)^2 + (-34)^2)`

`d = sqrt(144 + 1156)`

`d = sqrt(1300)`

`d = 10sqrt13`

If you want to leave it in exact form, you can leave the distance as `10sqrt13`. However, if you want the decimal answer, here it is rounded to the nearest thousandth's place:
`d ~~ 36.056`

Hope this helps!