SOLUTION: please help me find the distance between these two points and the midpoint of the line segment joining them (-1,1),(-1+3sqrt3,4

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Question 120516: please help me find the distance between these two points and the midpoint of the line segment joining them (-1,1),(-1+3sqrt3,4
Answer by solver91311(17077) About Me  (Show Source):
You can put this solution on YOUR website!
To find the distance between two points, use the distance formula:

d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29

In your case, for the points given:

d=sqrt%28%28%28-1%29-%28-1%2B3%2Asqrt%283%29%29%29%5E2%2B%281-4%29%5E2%29

d=sqrt%28%283%2Asqrt%283%29%29%5E2%2B%28-3%29%5E2%29

d=sqrt%2827%2B9%29=sqrt%2836%29=6

The x-coordinate of the midpoint between two points is given by %28x%5B2%5D-x%5B1%5D%29%2F2, or in this case x%5Bm%5D=%28%28-1%2B3%2Asqrt%283%29%29-%28-1%29%29%2F2=%283%2Asqrt%283%29%29%2F2

Likewise, the y-coordinate is given by: %28y%5B2%5D-y%5B1%5D%29%2F2, in this case, y%5Bm%5D=%284-1%29%2F2=3%2F2

Therefore, the midpoint is (%283%2Asqrt%283%29%29%2F2,3%2F2)