SOLUTION: For each pair of points find the distance between them and the midpoint of the line segment joining them. a) (a,0),(b,0) b) (π,0),(π/2,1) Thank you in advance!!

Algebra ->  Graphs -> SOLUTION: For each pair of points find the distance between them and the midpoint of the line segment joining them. a) (a,0),(b,0) b) (π,0),(π/2,1) Thank you in advance!!      Log On


   

Question 177740This question is from textbook College Algebra
: For each pair of points find the distance between them and the midpoint of the line segment joining them.
a) (a,0),(b,0)
b) (π,0),(π/2,1)
Thank you in advance!! This question is from textbook College Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.

a)
Distance:

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%28a-b%29%5E2%2B%280-0%29%5E2%29 Plug in x%5B1%5D=a,x%5B2%5D=b, y%5B1%5D=0, and y%5B2%5D=0


d=sqrt%28%28a-b%29%5E2%2B%280%29%5E2%29 Subtract


d=sqrt%28%28a-b%29%5E2%2B0%29 Square 0 to get 0


d=sqrt%28%28a-b%29%5E2%29 Simplify


d=abs%28a-b%29 Take the square root of the square to get the absolute value of original expression. Note: the distance is ALWAYS positive.


So the distance between the points (a,0),(b,0) is d=abs%28a-b%29



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Midpoint:

X-Coordinate of the Midpoint

x%5Bmid%5D=%28x%5B1%5D%2Bx%5B2%5D%29%2F2 Start with the x-mid formula


x%5Bmid%5D=%28a%2Bb%29%2F2 Plug in x%5B1%5D=a and x%5B2%5D=b


So the x-coordinate of the midpoint is x=%28a%2Bb%29%2F2

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Y-Coordinate of the midpoint

y%5Bmid%5D=%28y%5B1%5D%2By%5B2%5D%29%2F2 Start with the y-mid formula


y%5Bmid%5D=%280%2B0%29%2F2 Plug in y%5B1%5D=0, and y%5B2%5D=0


y%5Bmid%5D=0%2F2 Add


y%5Bmid%5D=0 Reduce


So the y-coordinate of the midpoint is 0


So this means that the midpoint of the segment with the endpoints (a,0),(b,0) is