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.
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