A point P moves on the line 2x -3y + 4 = 0. I | vedclass

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Question

Let point $P$ is $\left( {\alpha ,\beta } \right)\,$ and center of $\Delta PQR$ is $(h,k)$, then $3h = \alpha  + 1 + 3\,\,$ and&nb

Vedclass · Accepted Answer

with slope $\frac{2}{3}$

Vedclass · Answer

Let point $P$ is $\left( {\alpha ,\beta } \right)\,$ and center 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 $\left( {\alpha ,\beta } \right)$ lies on $2x-3y+4=0$

$ \Rightarrow 2\left( {3h - 4} \right) - 3\left( {k - 2} \right) + 4 = 0$

$ \Rightarrow $ losus is $6x-9y+2=0$ whose slope is $\frac{2}{3}$

A point $P$ moves on the line $2x -3y + 4 = 0$. If $Q(1, 4)$ and $R(3, -2)$ are fixed points, then the locus of the centroid of $\Delta PQR$ is a line

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