A) with slope \[\frac{3}{2}\]
B) parallel to x-axis
C) with slope \[\frac{2}{3}\]
D) parallel to y-axis
Correct Answer: C
Solution :
Let point P is \[(a,\beta )\]and centroid of \[\Delta PQR\] is (h, k), then \[3h=\alpha +1+3\]and \[3k=\beta +4-2\] |
\[\Rightarrow \] \[\alpha =3h-4\]and \[\beta =3k-2\] |
Because \[(\alpha ,\beta )\]lies on \[2x-3y+4=0\] |
\[\Rightarrow \]\[2(3h-4)-3(k-2)+4=0\] |
\[\Rightarrow \]locus is\[6x-9y+2=0\] whose slope is\[\frac{2}{3}\]. |
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