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Midpoint of u

The midpoint of u is in the middle of t and v. T is 3x+9 and v is 14+2x. what is Tu, tv, and uv?

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Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
4.9 4.9 (115 lesson ratings) (115)
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TV = 3x+9 - (14+2x)
TV = 3x + 9 -14 - 2x
TV =  x - 5 
 
U = ((3x + 9) + (14 + 2x)) / 2 
U = (5x + 23) / 2
 
TU = (2(3x + 9) / 2) - (5x+23)/2 
 
TU = (6x + 18 - 5x -23) /2 
 
TU = (x - 5) / 2
 
 
Since U is the midpt, UV = TU, so UV = (x-5) / 2
 
TU + UV = TV 
 
(x-5) / 2 + (x-5) /2 = 2 (x-5) /2 = x-5 = TV
 
 
 
Use a number for x.  Let's use 10.
 
T is 39, V = 34
U = (39 + 34)/2 = 73/2 = 36.5
 
TV = 39-34 = 5
TV from our equation is x-5.  10 - 5 = 5.   Good.
 
 
TU and UV = (x-5) / 2.   (10-5) /2 = 5/2.
(39-34)/2 = 5/2   Good.
 
Alan B. | Problem Solving in Physics, Astronomy, Statistics, Java, Math, UNIXProblem Solving in Physics, Astronomy, S...
5.0 5.0 (81 lesson ratings) (81)
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The midpoint formula of points x1,y1 and x2,y2 is given by (x1+x2)/2,(y1+y2)/2.
 
So the midpoint of 7,12 and 13,20 would be 10,16.