A) parallel to y-axis
B) with slope \[\frac{2}{3}\]
C) parallel to x-axis
D) with slope \[\frac{3}{2}\]
Correct Answer: B
Solution :
\[P\left( h,\,\,\frac{2h+4}{3} \right)\] \[Q\text{ }\left( 1,\text{ }4 \right)\text{ }Q\left( 3,\text{ }-2 \right)\] Centroid G \[(\alpha ,\,\,\beta )\,\equiv \,\left( \frac{h+4}{3},\,\,\frac{2h+4+12-6}{9} \right)\] \[\alpha \,=\,\frac{h+4}{3};\,\,\beta =\frac{2h+10}{9};\,\,\beta \,=\,\frac{2(3\alpha -4)+10}{9};\]\[9\beta =6\alpha +2\] Locus \[\alpha \,=\,x;\,\,\beta =y;\,\,y=\frac{2}{3}x+\frac{2}{9}\] Slope \[=\frac{2}{3}\]
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