Question

What is the distance between `(-4, 11)` and #(5, 6) #?

Answer 1

The distance is `sqrt106` or about `10.296` (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((5-(-4))^2 + (6-11)^2)`

Now we simplify:
`d = sqrt((9)^2 + (-5)^2)`

`d = sqrt(81 + 25)`

`d = sqrt(106)`

If you want to leave it in exact form, you can leave the distance as `sqrt106`. However, if you want the decimal answer, here it is rounded to the nearest thousandth's place:
`d ~~ 10.296`

Hope this helps!