+55 Hi, may I please have some help on the following problem? Thanks so much!
Let \(X\), \(Y\), and \(Z\) be points such that \(\frac{XZ}{XY} = \frac{ZY}{XY}=\frac12. \) If \(Y=(1,7)\), \(Z=(-1,-7)\), then what is the sum of the coordinates of \(X\)?
+129852 Since XZ/XY = 1/2 and ZY/XY = 1/2......we can see that Z is the midpoint of XY
To find this point we have that
x value of Z = [ x yalue of X + x value of Y ] / 2
-1 = [ x value of X + 1 ] / 2 multipy both sides by 2
-2 = x value of X + 1 suvtract 1 from both sides
-3 = x value of X
Also
y value of of Z = [ y value of X + y value of Y ] / 2
- 7 = [ y value of X + 7] / 2 multiply both sides by 2
-14 = y value of X + 7 subtract 7 from both sides
-21 = y value of X
So X = (-3, -21) and the sum of the its coordinates = -24
