SOLUTION: (-6,-4),(3,4) FIND THE DISTANCE BETWEEN EACH PAIR OF POINTS AND THE MIDPOINT OF THE LINE SEGMENT JOINING THE POINTS. LEAVE DISTANCE IN RADICAL FORM. THANKS

Algebra ->  Linear-equations -> SOLUTION: (-6,-4),(3,4) FIND THE DISTANCE BETWEEN EACH PAIR OF POINTS AND THE MIDPOINT OF THE LINE SEGMENT JOINING THE POINTS. LEAVE DISTANCE IN RADICAL FORM. THANKS      Log On


   

Question 104648: (-6,-4),(3,4) FIND THE DISTANCE BETWEEN EACH PAIR OF POINTS AND THE MIDPOINT OF THE LINE SEGMENT JOINING THE POINTS. LEAVE DISTANCE IN RADICAL FORM. THANKS
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"FIND THE DISTANCE BETWEEN EACH PAIR OF POINTS"


Start with the given distance formula
d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 where is the first point and is the second point

d=sqrt%28%28-6-3%29%5E2%2B%28-4-4%29%5E2%29 Plug in x%5B1%5D=-6, x%5B2%5D=3, y%5B1%5D=-4, y%5B2%5D=4

d=sqrt%28%28-9%29%5E2%2B%28-8%29%5E2%29 Evaluate -6-3 to get -9. Evaluate -4-4 to get -8.

d=sqrt%2881%2B64%29 Square each value

d=sqrt%28145%29 Add

So the distance approximates to

d=12.0415945787923

which rounds to
12.04

So the distance between (-6,-4) and (3,4) is approximately 12.04 units




"FIND THE MIDPOINT OF THE LINE SEGMENT JOINING THE POINTS"


In order to find the midpoint between the points (-6,-4) and (3,4), 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
x%5Bmid%5D=%28-6%2B3%29%2F2=%28-3%29%2F2=-1.5


So the x-coordinate of the midpoint is -1.5 (i.e. x=-1.5)
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To find , average the y-coordinates between the two points
y%5Bmid%5D=%28-4%2B4%29%2F2=%280%29%2F2=0


So the y-coordinate of the midpoint is 0 (i.e. y=0)
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Answer:
Since the coordinates of the midpoint are x=-1.5, y=0, this means the midpoint is (-1.5,0)

Check:
Here is a graph to visually see the answer
Graph of the line segment with the endpoints (-6,-4) and (3,4) with the midpoint (-1.5,0)



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, so our answer is verified.