Midpoint of u

Question

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?

Answer 1

 

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.

 

Answer 2

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.