What is the distance between (13,-14,1) and (12,-21,6)?

1 Answer
Tony B
May 14, 2016

d=5sqrt(3)" " Exactly

d= 8.660" " to 3 decimal places

Explanation:

This is the coordinate system for 3-space. When it is broken down into projections onto the planes you end up with two triangles that are linked by a common side. Consequently we can turn to that good old favourite: Pythagoras.

Let the distance between points be d

d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)

d=sqrt( (12-13)^2+(-21-(-14))^2+(6-1)^2)

d=sqrt(75) = sqrt(5^2xx3)
d=5sqrt(3)" " Exactly

d= 8.660" " to 3 decimal places

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