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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

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

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
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.

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