Saturday

November 22, 2014

November 22, 2014

Posted by **Greg** on Friday, September 14, 2012 at 2:35pm.

a - pick 2 arbitrary points in 3 dimensions, (x1, y1, and Z1) and (x2,y2,z2) and plot these points. Not that there are 0- degrees between the xy, xz, and yz axes.

b- using your sketch from part a, find the distance between these 2 points, generalize the above equation to 3 dimensions.

- Precalculus -
**Steve**, Friday, September 14, 2012 at 2:49pmfirst, the axes are perpendicular, the there are 90°, not 0° between axes.

Second, can't do plots here.

Third, once you have picked your points, just plug them into the 3D version of the formula:

d^2 = (x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2

To see that this is true, consider just the distances in the plane z=z1.

w^2 = (x2-x1)^2+(y2-y1)^2

That's just a diagonal line of length w. To get from (x1,y1,z1) to (x2,y2,z2), consider the right triangle from (x1,y1,z1) to (x2,y2,z1) with length w, and go from there to (x2,y2,z2) of length (z2-z1).

If that's confusing, just look online for references to 3D distances.

http://tonto.stanford.edu/~brian/euclidean_distance_in.html

is a good place to start

**Answer this Question**

**Related Questions**

Precalculus - he distance between 2 points (x1,Y1) and (x2,y2) is given by d = ...

GEOMETRY - POINTS M,N, AND O ARE 3 POINTS ON A LINE WITH COORDINATE 5, 2 SQUARE...

c++ - Distance between two 3-D points. Given two points in space (3-dimensional...

Precalculus - 1. Simplify the expression ((5x^-2)/(4x^2))^-2 2. (x)/(x^2-81)-(9...

math - 4. Point E is located at (–2, 2) and point F is located at (4, –6). What ...

math - 4. Point E is located at (–2, 2) and point F is located at (4, –6). What ...

math - 4. Point E is located at (–2, 2) and point F is located at (4, –6). What ...

geometry CA - Graph quadrilateral ABCD. Then determine the most precise name for...

math - Point E is located at (-2,2) and point F is located at (4,-6).What is the...

pre-alg - point E is located at (-2,2) and point F is located at (4,-6). what is...