let X, Y, and Z be points such that XZ/XY = ZY/XY = 1/2 . if Y= (1, 7) , Z= (-1, -7), then what is the sum of the coordinates of X?
+128407 If XZ/XY = ZY/XY = 1/2
Then XZ = ZY
Then Z must be the midpoint of XY
So
[ 1 + x coord of X ] / 2 = -1 multiply through by 2
1 + x coord of X = -2 subtract 1 from both sides
x coord of X = - 3
And
[ 7 + y coord of X ] / 2 = -7
7 + y coord of Y = -14 subtract 7 from both sides
y coord of Y = -21
So X = (-3, -21) and the sum of the coordinates = -24
