Let A(6,−5) and B(−6,1) be the two vertices of the triangle ABC, if the locus of centroid of △ABC is 2x+5y=1, then the locus of vertex C is
A
5x−2y=17
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B
2x+5y=23
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C
2x−5y=21
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D
5x+2y=19
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Solution
The correct option is B2x+5y=23 Let the coordinates of C be (a,b), then the coordinates of centroid are (a+6−63,b−5+13)=(a3,b−43) Since, the centroid has the locus 2x+5y=1, then 2(a3)+5(b−43)=1 2a+5(b−4)=3 2a+5b=23 Therefore the locus of vertex C(a,b) is 2x+5y=23.