coordinate geometry
posted by muna .
the three points g(4,0) ,h(h,6) and i(7,1) are such that gh is twice as long as gi .calculate the two possible values of h.

gi^2 = 3^2+1^2 = 10^2
gh^2 = 4 * 10^2
4*10^2 = (h4)^2 + 36
400 = h^2  8h + 36
h^2  8 h  364 = 0
h = [ 8 +/ sqrt(64+1456) ]/2
h = 4 +/ 19.5
h = 23.5 or 15.5
check my arithmetic ! 
using distance formula
d of GI= square root of 103.1622
twice this is the square root of 40
could be 6 or 2
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