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Let X, Y, and Z be points such that If XZ/XY = ZY/XY = 1/2.  If Y = (1,-7) and Z = (-1,-7), then what is the sum of the coordinates of X?

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Y=(1, -7)       Z=(-1, -7)

X = (-3, -7)

Sum of coordinates of X = -10

Assume   that  the points  are  in  this order   XZY

XZ  =   ZY

So

X =    [  -1 -  ( 1 - - 1)   ,  -7 - ( -7 - - 7) ]   =  [ -1-2 , -7 - 0 ]  =  ( -3, -7)

Sum of coordinates =   -10