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 and calculating gives:
d = sqrt((color(red)(5) - color(blue)(3))^2 + (color(red)(-8) - color(blue)(-2))^2 + (color(red)(-16) - color(blue)(-12))^2)d=√(5−3)2+(−8−−2)2+(−16−−12)2
d = sqrt((color(red)(5) - color(blue)(3))^2 + (color(red)(-8) + color(blue)(2))^2 + (color(red)(-16) + color(blue)(12))^2)d=√(5−3)2+(−8+2)2+(−16+12)2
d = sqrt(2^2 + (-6)^2 + (-4)^2)d=√22+(−6)2+(−4)2
d = sqrt(4 + 36 + 16)d=√4+36+16
d = sqrt(56) = 7.48d=√56=7.48 rounded to the nearest hundredth.
