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?
+128474 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
