SOLUTION: find the length and midpoint of the line segment connecting (-4,3) and (3,5). thanks for the help!

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Question 179078: find the length and midpoint of the line segment connecting (-4,3) and (3,5).
thanks for the help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Length



d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 Start with the distance formula.


d=sqrt%28%28-4-3%29%5E2%2B%283-5%29%5E2%29 Plug in x%5B1%5D=-4, x%5B2%5D=3, y%5B1%5D=3, and y%5B2%5D=5.


d=sqrt%28%28-7%29%5E2%2B%283-5%29%5E2%29 Subtract 3 from -4 to get -7.


d=sqrt%28%28-7%29%5E2%2B%28-2%29%5E2%29 Subtract 5 from 3 to get -2.


d=sqrt%2849%2B%28-2%29%5E2%29 Square -7 to get 49.


d=sqrt%2849%2B4%29 Square -2 to get 4.


d=sqrt%2853%29 Add 49 to 4 to get 53.


So our answer is d=sqrt%2853%29


Which approximates to d=7.28


So the distance between the two points is approximately 7.28 units.


This means that the length of the segment is about 7.28 units.





Midpoint



To find the midpoint, first we need to find the individual coordinates of the midpoint.


X-Coordinate of the Midpoint:




To find the x-coordinate of the midpoint, simply average the two x-coordinates of the given points by adding them up and dividing that result by 2 like this:


x%5Bmid%5D=%28-4%2B3%29%2F2=-1%2F2


So the x-coordinate of the midpoint is x=-1%2F2


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Y-Coordinate of the Midpoint:




To find the y-coordinate of the midpoint, simply average the two y-coordinates of the given points by adding them up and dividing that result by 2 like this:


y%5Bmid%5D=%283%2B5%29%2F2=8%2F2=4


So the y-coordinate of the midpoint is y=4


So the midpoint between the points and is