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in the diagram, point Y is the midpoint of seg. XZ, XY = 3a +1, & YZ = a+9 for some constant, a. find the length of segment XZ. Pls help

 

 Sep 24, 2020
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Since  Y  is the midpoint of  XZ,  it must be that

 

the length of  XY   =   the length of  YZ

 

which means

 

3a + 1   =   a + 9        Let's solve this equation for a.

                                  Subtract  a  from both sides of the equation.

2a + 1   =   9

                                  Subtract  1  from both sides of the equation.

2a   =   8

                                  Divide both sides of the equation by  2

a   =   4

 

Now that we know what  a  is,  we can find the length of  XZ.

 

the length of  XZ   =   3a + 1  +  a + 9

 

the length of  XZ   =   3(4) + 1  +  4 + 9

 

the length of  XZ   =   12 + 1  +  4 + 9

 

the length of  XZ   =   ?

 Sep 25, 2020

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