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In square ABCD shown, X is the midpoint of BC and Y is the midpoint of AX. If CZ:ZD=3:1 and the side length of the square is 5 units, find YZ.

 

 Jan 24, 2021
 #1
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Let A   = (0,5)

Let  X  =  (5,2.5)

Y =    [ (5 + 0)/2    ,   ( 2.5 + 5)  /2   ]  =    (2.5, 3.75)

 

CZ  =  (  1 / (1 + 3)  *  5   ,  0  )   =   (5/4 , 0) =  (1.25, 0)

 

So

 

YZ  = sqrt  [ ( 1.25 - 2.5)^2  + 3.75^2  ]  =  sqrt  [ 1.25^2  + 3,75^2  ]   =  sqrt (125/8)  =  5sqrt (5) / ( 2 sqrt (2) =

 

(5/2) sqrt ( 2.5)   = 2.5sqrt (2.5)  ≈  3.953

 

 

cool cool cool

 Jan 24, 2021

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