Question 223861
<hr />At least you're trying.  That's the most important thing.


With a problem like this, your only hope of getting it is to draw pictures.  PLEASE IGNORE ALL NUMBERS.
"Suppose point T is the midpoint of RS"
{{{number_line(600, -10, 10, R=-8, S=8, T=0)}}}


" . . . and point W is the midpoint of RT"
{{{number_line(600, -10, 10, R=-8, S=8, T=0, W=-4)}}}


"If XY is equivalent to RT "
{{{number_line(600, -10, 10, X=-8, Y=0)}}}


"and TS has a length of z"
{{{number_line(600, -10, 10, S=8, T=0)}}}


"write the length of the segment in terms of z for RT."
{{{number_line(600, -10, 10, R=-8, T=0)}}}


The numbers make it harder to see, but I hope you can tell that XY is equivalent to TS.  So, in terms of z, XY equals {{{1z}}}.  It seems complicated, because of the way it's written, but it's not complicated.  If they want some written proof, I suppose you could say that since T is the midpoint, then RT is equivalent to TS.  And XY is equivalent to RT (given).  Therefore, XY must be equivalent to TS.


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