A point P moves on the line 2 x -3 y -4-0- If Q 1-4 and R 3-2 are fixed points- then the locus of the centroid of - PQR is a line -A- parallel to x-axis -B- with slope 1- -C- parallel to y-axis 2D- with slope 4-3

Let the centroid of the Δ PQR is C (α,β) ∴α=h+1+33⇒ h=3α 4 nbsp; β=4+k 23⇒ k=3β 2 P(h,k) passes through the line nbsp;2x 3y+4=0 ∴ 2(3α 4) 3(3β 2)+4=0 nb ...

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Byju's Answer

Standard XII

Mathematics

Centroid

A point P mov...

Question

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

parallel to x-axis

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parallel to y-axis

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with slope

\frac{3}{2}

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with slope

\frac{2}{3}

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Solution

The correct option is D with slope $\frac{2}{3}$

Let the centroid of the $Δ P Q R$ is $C (α, β)$
$∴ α = \frac{h + 1 + 3}{3} \Rightarrow h = 3 α - 4$
$β = \frac{4 + k - 2}{3} \Rightarrow k = 3 β - 2$
$P (h, k)$ passes through the line $2 x - 3 y + 4 = 0$
$∴ 2 (3 α - 4) - 3 (3 β - 2) + 4 = 0$
$\Rightarrow 6 α - 9 β + 2 = 0$
Hence, the locus is $6 x - 9 y + 2 = 0$
$∴$ slope $= \frac{6}{9} = \frac{2}{3}$

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Similar questions

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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 ΔPQR is a line :

The correct option is D with slope 23 Let the centroid of the ΔPQR is C(α,β) ∴α=h+1+33⇒h=3α−4 β=4+k−23⇒k=3β−2 P(h,k) passes through the line 2x−3y+4=0 ∴ 2(3α−4)−3(3β−2)+4=0 ⇒6α−9β+2=0 Hence, the locus is 6x−9y+2=0 ∴ slope =69=23

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