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a right angled isoceles triangle with side 1 1 root2 is given
its hypotenoius slips on coordinate axis
find the locus of its centroid

saliem89 , 9 Years ago
Grade 11
anser 1 Answers
Vikas TU
Assume hypertenuse lying on coordinate axes as having points 
(a,0) and (0,b).
The other coordinate of right angle triangle as issoceles will be then (a,b)
And let centroifd of the triangle be (h,k)
Now interpret the relations between these parameters and solve.
 
h = 2a/3 or a = 3h/2--------------------(1)
k = 2b/3 or b = 3k/2--------------(2)
 
Now from Pyhogorus
Hypertenuse^2 = a^2 + b^2 = 484 (given.)---------------------(3)
from eqns. (!) and (2)
put in (3)
 
h^2 + k^2 = 484*4/9
 
or
 
x^2  + y^2 = 484*4/9
hence locus is circle.
Last Activity: 9 Years ago
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