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=√(x2−x1)2+(y2−y1)2+(z2−z1)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=√(−1−8)2+(−3−−4)2+(5−6)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=√(−1−8)2+(−3+4)2+(5−6)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.