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A point P moves on line 2x-3y+4=0 If Q(1...

A point P moves on line `2x-3y+4=0` If `Q(1,4)` and `R(3,-2)` are fixed points, then the locus of the centroid of `triangle PQR` is a line: (a) with slope `3/2` (b) parallel to y-axis (c) with slope `2/3` (d) parallel to x-axis

A

parallel to x-axis

B

with slope `3/2`

C

parallel to y-axis

D

with slope `2/3`

Text Solution

Verified by Experts

The correct Answer is:
D

`4x - 6y + 5 = 0`
` Q(1,3) , P (3, - 1)`
Let (h,k) be centroid
`h = (t + 1 + 3)/( 3) = ( t+ 4)/(3)`
`k = ((4t + 5)/(6) + 3 - 1)/(3) = ((4t + 5 + 12)/(6) )/(3) = (4t + 17)/(18)`
`t = 3h - 4`
` 18k - 17 = 4t`
` 18 k = 17 = 4 (3h - 4)`
` 18k - 17 = 12h - 16`
` 12h - 18k + 1 = 0`
` 12 x - 18 y + 1 = 0`
Slope ` = (12/18) = 2/3`
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