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

 Feb 7, 2019
 #1
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We must have this orientation :

 

X       Z       Y

 

So...if XZ/XY = 1/2     and ZY/XY = 1/2

 

Then Z must be the midpoint of XY......so we have that

 

[ 1 + x coordinate of X ] / 2  =  x coordinate of Z

[ 1 +  xX] / 2 = -1       multiply both sides by 2

1 + xX  = -2       subtract 1 from both sides

xX = -3

 

Likewise

 

[ 1 + y coordinate of X ] / 2 =  y coordinate of Z

[ 1 + yX ] / 2 =  -7     multiply both sides by 2

1 + yX  = -14    subtract 1 from both sides

yX = - 15

 

So

 

X  = ( -3, -15)

 

And the sum of these  =   -18

 

 

cool cool cool

 Feb 7, 2019

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