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A straight rod of length 9 units slides with its ends A,B always on the x and y axes respectively.then the locus of the centroid of triangle OAB is

A straight rod of length 9 units slides with its ends A,B always on the x and y axes respectively.then the locus of the centroid of triangle OAB is

Grade:8

1 Answers

shreyan fernandes
13 Points
6 years ago
Let the  co ordinates of centroid be (h,k).
h=(0+x1+0)/3
k=(0+0+y1)/3

so, x1=3h and y1=3k
Now length of the rod AB=9 units
 (Plot it on a paper and label the triangle AOB, where A=(x1,0) and B=(0,y1) )

Now in triangle OAB

OA2+OB2=AB2

x12+y12=92

(SUBSTITUTE THE VALUE OF x1 and y1)

(3h)2+(3k)2=81

on dividing the whole of the above equation by 9 we get,

h2+k2=9

now replace h by x and k by  y to get the locus

therefore we get a circle of radius 3units

x2+y2=9   (Answer)

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