Question

What is the distance between `(5,-3)` and `(3,7)`?

Answer 1

The distance is `2sqrt26` or about `10.198` (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 - 5)^2 + (7 - (-3))^2)`

Now we simplify:
`d = sqrt((-2)^2 + (10)^2)`

`d = sqrt(4 + 100)`

`d = sqrt(104)`

`d = 2sqrt26`

If you want to leave it in exact form, you can leave the distance as `2sqrt26`. However, if you want the decimal answer, here it is rounded to the nearest thousandth's place:
`d ~~ 10.198`

Hope this helps!