Question

What is the distance between `(4, –1, 2)` and `(4, –4, –2)`?

Answer 1

`5`

Explanation:

In general, the distance between points `(x_1, y_1, z_1)` and `(x_2, y_2, z_2)` is given by the distance formula:

`d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2)`

In our particular example, we have `x_1 = x_2` and this simplifies to what is basically a `3,4,5` right angled triangle, but evaluating the formula directly we get:

`d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2)`

`=sqrt((4-4)^2+(-4-(-1))^2+(-2-2)^2)`

`=sqrt(0^2+(-3)^2+(-4)^2)`

`=sqrt(0+9+16)`

`=sqrt(25)`

`=5`