Question

in triangle pqr,P=(6,5),midpoint of QR is (9,-1) find coordinates of centroid​

Answer 1

Answer:Let co-ordinates of point R is(a,b).

If, (h,k) the centroid, then we can say that

h=2+4+a3andk=5−11+b3→(1) As point, R is passing through line N fiven by 9x+7y+4=0, we can have,

b=−4−9a7

Now, putting value of b in (1),

h=6+a3 and k=−6−(4+9a)73

h=6+a3 and k=−46−9a21

a=3h−6 and a=−21k+469

Thus,−21k+469=3h−6

⇒27h+21k−8=0

⇒9h+7k−83=0 that is clearly parallel to line N. So, option D is the correct option

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Answer 2

(6,5) and (9,-1)are in ratio 2:1 at centroid
Therefore { (6*1+9*2)/2+1 , (5*1+2*-1)/2+1}
(24/3,3/3 )
(8,1)