Question

What is the distance between `(2, 5)` and # ( 7, 4) #?

Answer 1

The distance is `sqrt26` or about `5.099` (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((7-2)^2 + (4-5)^2)`

Now we simplify:
`d = sqrt((5)^2 + (-1)^2)`

`d = sqrt(25 + 1)`

`d = sqrt(26)`

If you want to leave it in exact form, you can leave the distance as `sqrt26`. However, if you want the decimal answer, here it is rounded to the nearest thousandth's place:
`d ~~ 5.099`

Hope this helps!