What is the distance between (8,-4,6)(8,4,6) and (-1,-3,5)(1,3,5)?

1 Answer
Mar 13, 2018

See a solution process below:

Explanation:

The formula for calculating the distance between two points is:

d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2 + (color(red)(z_2) - color(blue)(z_1))^2)d=(x2x1)2+(y2y1)2+(z2z1)2

Substituting the values from the points in the problem gives:

d = sqrt((color(red)(-1) - color(blue)(8))^2 + (color(red)(-3) - color(blue)(-4))^2 + (color(red)(5) - color(blue)(6))^2)d=(18)2+(34)2+(56)2

d = sqrt((color(red)(-1) - color(blue)(8))^2 + (color(red)(-3) + color(blue)(4))^2 + (color(red)(5) - color(blue)(6))^2)d=(18)2+(3+4)2+(56)2

d = sqrt(-9^2 + 1^2 + (-1)^2)d=92+12+(1)2

d = sqrt(81+ 1 + 1)d=81+1+1

d = sqrt(83)d=83

Or

d = 9.110d=9.110 rounded to the nearest thousandth.