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 $\triangle \mathrm{PQR}$ is a line :
parallel to $x$-axis
with slope $\frac{2}{3}$
with slope $\frac{3}{2}$
parallel to $\mathrm{y}$-axis
Correct Option: , 2
Solution:
Let the centroid of $\triangle \mathrm{PQR}$ is $(\mathrm{h}, \mathrm{k}) \& \mathrm{P}$ is $(\alpha, \beta)$, then
$\frac{\alpha+1+3}{3}=\mathrm{h} \quad$ and $\quad \frac{\beta+4-2}{3}=\mathrm{k}$
$\alpha=(3 h-4) \quad \beta=(3 k-4)$
Point $P(\alpha, \beta)$ lies on line $2 x-3 y+4=0$
$\therefore 2(3 h-4)-3(3 k-2)+4=0$
$\Rightarrow$ locus is $6 x-9 y+2=0$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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