How do I find the Euclidean distance between one point and all the points in a list?

Question

I want to find the Euclidean distance between one point (x1) and a list of points (y1), which contains a lot of coordinates

x1 = killer[[2]]

{6.05102, 5.87667}

y1 = victim[[2 ;;]]

{{1.40687, 4.92494}, {0.419206, 1.70406}, {6.29657,0.577941}, {4.12022, 4.94952},
{2.04784, 5.94545}, {1.29192,1.43152}, {3.26737, 1.90134}, {4.27274, 0.528028},
{2.79659,1.37788}, {5.43955, 1.81355}}

Is it possible for me to find the EuclideanDistance between x1 and y1, where it will show all results between x1 and each elements in y1.

Answer 1

Here is what you want to do. Let the first point's coordinate be stored as a list of list as follows:

x1 = {{6.05102, 5.87667}}    

and the second set of coordinates

y1 = {{1.40687, 4.92494}, {0.419206, 1.70406}, {6.29657,0.577941}, {4.12022, 4.94952},
      {2.04784, 5.94545}, {1.29192,1.43152}, {3.26737, 1.90134}, {4.27274, 0.528028},
      {2.79659,1.37788}, {5.43955, 1.81355}} 

Now to compute the Euclidean distances between x1 and every element in y1 use Outer, your best friend from now on.

Outer[EuclideanDistance, x1, y1, 1]//Flatten

This then gives you

{4.74067, 7.00914, 5.30442, 2.14187, 4.00377, 6.51217, 4.85304, 5.63651, 5.55252, 4.10887}. 

Hope this helps. In fact, you can loop this through various x1's as follows.

Table[Outer[EuclideanDistance, {killer[[k]]}, y1, 1], {k, 1, n}]

Where n is the Length of the killer list. This is fast and compact code.