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 is a line: |
|||

(a) |
Parallel to x-axis |
(b) |
with slope |

(c) |
with slope |
(d) |
Parallel to y-axis |

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 is a line: |
|||

(a) |
Parallel to x-axis |
(b) |
with slope |

(c) |
with slope |
(d) |
Parallel to y-axis |

1 Answer

127 votes

Let the centroid of is (h, k) & P is (), then

= h and

= (3h − 4) = (3k − 4)

Point P() lies on line 2x − 3y + 4 = 0

2(3h − 4) − 3(3k − 2) + 4 = 0

⇒ locus is 6x − 9y + 2 = 0

127 votes

127