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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 \(X\)?

 Nov 13, 2020
 #1
avatar+114221 
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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

 

 

cool cool cool

 Nov 13, 2020

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