Question:
Two vertices of a triangle are $(0,2)$ and $(4,3)$. If its orthocentre is at the origin, then its third vertex lies in which quadrant ?
Fourth
Second
Third
First
Correct Option: , 2
Solution:
$\mathrm{m}_{\mathrm{BD}} \times \mathrm{m}_{\mathrm{AD}}=-1 \Rightarrow\left(\frac{3-2}{4-0}\right) \times\left(\frac{\mathrm{b}-0}{\mathrm{a}-0}\right)=-1$
$\Rightarrow b+4 a=0$ ...............(I)
$\mathrm{m}_{\mathrm{AB}} \times \mathrm{m}_{\mathrm{CF}}=-1 \Rightarrow\left(\frac{(\mathrm{b}-2)}{\mathrm{a}-0}\right) \times\left(\frac{3}{4}\right)=-1$
$\Rightarrow 3 b-6=-4 a \Rightarrow 4 a+3 b=6 \quad \ldots \ldots$ (ii)
From (i) and (ii)
$a=\frac{-3}{4}, b=3$
$\therefore \quad$ II ${ }^{\text {nd }}$ quadrant.
Option (2)
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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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