length and midpoint

Question

Find the length and midpoint of the segment with the given (-7,-10 9), (-2,9,-9)

Answer 1

Length via the distance formula:

sqrt ( (-7 - -2)^2 + (-10 - 9)^2 + (9 - -9)^2 ) =

sqrt( (-5)^2 + (-19)^2 + 18^2) =

sqrt ( 25 + 361 + 324 ) =

sqrt ( 710 ) =

sqrt( 71 * 10) =

sqrt( 71 * 5 * 2), which cannot be simplified further because 71 is prime

So the distance is EXACTLY sqrt(710) which is APPROXIMATELY 26.64582518894845560793259882791..