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Question

Let A(2,3) and B(2,1) be two angular points of ABC. If the centroid of the triangle moves on the line 2x+3y=1, then the locus of the angular point C is given by

A
2x+3y=9
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B
2x3y=9
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C
3x+2y=5
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D
3x2y=3
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Solution

The correct option is A 2x+3y=9
Let the coordinate of the angular point C be (h,k)
Then, coordinates of the centroid is (22+h3,3+1+k3)=(h3,k23)
Centroid lies on the line 2x+3y=1
2(h3)+3(k23)=1
2h+3k=9
So locus will be 2x+3y=9

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