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)(5) - color(blue)(1))^2 + (color(red)(4) - color(blue)(-3))^2 + (color(red)(-3) - color(blue)(2))^2)d=√(5−1)2+(4−−3)2+(−3−2)2
d = sqrt((color(red)(5) - color(blue)(1))^2 + (color(red)(4) + color(blue)(3))^2 + (color(red)(-3) - color(blue)(2))^2)d=√(5−1)2+(4+3)2+(−3−2)2
d = sqrt(4^2 + 7^2 + (-5)^2)d=√42+72+(−5)2
d = sqrt(16 + 49 + 25)d=√16+49+25
d = sqrt(90) = 9.487d=√90=9.487
