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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?

Guest Feb 7, 2019

#1**+1 **

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

CPhill Feb 7, 2019