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.

Answer 1

gi^2 = 3^2+1^2 = 10^2

gh^2 = 4 * 10^2

4*10^2 = (h-4)^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 !

Answer 2

using distance formula

d of GI= square root of 10-3.1622

twice this is the square root of 40

could be- 6 or 2