Question

What is the distance between `(-4,-3,4)` and `(-30,15,-16)`?

Answer 1

`quadcolor(red)(d = 10sqrt14)` or `color(red)(~~37.417)` (rounded to thousandth's place)

Explanation:

The distance between three dimensions is similar to the distance between two dimensions.

We use the formula:
`quadcolor(red)(d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2))`, where `x`, `y`, and `z` are the coordinates.

Let's plug in the values for the coordinates into the formula. Pay attention to the negative signs:
`quadd = sqrt((-30-(-4))^2 + (15-(-3))^2 + (-16-4)^2)`

And now simplify:
`quadd = sqrt((-26)^2 + (18)^2 + (-20)^2)`

`quadd = sqrt(676 + 324 + 400)`

`quadd = sqrt(1400)`

`quadd = sqrt(100 * 14)`

`quadd = sqrt100sqrt14`

`quadd = 10sqrt14`

`quadcolor(red)(d = 10sqrt14)` or `color(red)(~~37.417)` (rounded to thousandth's place)

Hope this helps!