Asked by Paula
In the figure shown above (its a right triangle), points G, H, and I in the xy-plane have coordinates of (0,2), (2,8) and (8,n), respectively if GH=HI what is the value of n?
Answers
Answered by
Reiny
since GH = HI then GI must be the hypotenuse
and GH is perpendicular to HI
slope GH = 3
slope of HI = (n-8)/6
(n-8)/6 = -1/3
3n-24 = -6
3n = 18
n = 6
check: plot the point I(8,6)
the slopes of GH and HI are 3 and -1/3, so right angle at H
GI = √(8^2 + 4^2 = √80 = 4√5
GH = √2^2 + 6^2) = √40
HI = √(6^2 + 2^2) = √40
is (√40)^2 + (√40)^2 = (√80)^2 ??, YES it is
and GH is perpendicular to HI
slope GH = 3
slope of HI = (n-8)/6
(n-8)/6 = -1/3
3n-24 = -6
3n = 18
n = 6
check: plot the point I(8,6)
the slopes of GH and HI are 3 and -1/3, so right angle at H
GI = √(8^2 + 4^2 = √80 = 4√5
GH = √2^2 + 6^2) = √40
HI = √(6^2 + 2^2) = √40
is (√40)^2 + (√40)^2 = (√80)^2 ??, YES it is
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