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Question

# Let A (2,-3) and B(-2,1) be the vertices of a tirangle ABC. If the centroid of this triangle moves on the line 2x+3y=1, then the locus of the vertex C is the line

A
2x+3y=9
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B
5x-3y=7
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C
3x+2y=5
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D
3x-2y=3
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Solution

## The correct option is A 2x+3y=9Let (x,y) be the coordinates of the vertex C and (x1,y1) be the coordinates of the centroid of the triangle, therefore x1=x+2−23y1=y−3+13 or x1=x3 and y1=y−23 the centroid lies on the line 2x+3y=1.So x1 and y1 satisfy the equation of the line. Thus 2x1+3y1=1⇒2(x3)+2(y−23)=12x+3y=9 The above equation is the locus of the vertex C.

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