Question 133211: Find the distance between the points, and find the midpoint of the line segment joining them? (9,8) and (2,1)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! First let's find the distance
Start with the given distance formula
 where ) is the first point ) and ) is the second point )
 Plug in  ,  ,  , 
 Evaluate  to get 7. Evaluate  to get 7.
 Square each value
 Add
 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
So the distance approximates to
which rounds to
9.89949
So the distance between (9,8) and (2,1) is approximately 9.89949 units
Now let's find the midpoint
In order to find the midpoint between the points (9,8) and (2,1), we need to average each corresponding coordinate. In other words, we need to add up the corresponding coordinates and divide the sum by 2.
So lets find the averages between the two points
To find  , average the x-coordinates between the two points
So the x-coordinate of the midpoint is 5.5 (i.e. x=5.5)
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To find  , average the y-coordinates between the two points
So the y-coordinate of the midpoint is 4.5 (i.e. y=4.5)
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Answer:
Since the coordinates of the midpoint are x=5.5, y=4.5, this means the midpoint is (5.5,4.5)
Check:
Here is a graph to visually see the answer
 Graph of the line segment with the endpoints (9,8) and (2,1) with the midpoint (5.5,4.5)
We could visually verify our answer if we simply draw right triangles from each point like this:
Here we can see that the two triangles are congruent (they both have a right angle and equal leg lengths), so our answer is verified.
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