Find the equation of the line passing through ( - 3, 5) and perpendicular to the line through the points (2, 5) and ( - 3, 6).
Given: The line perpendicular to the line passing through $(2,5)$ and $(-3,6)$ passes through $(-3,5)$.
Formula to be used: If $(a, b)$ and $(c, d)$ are two points then the equation of the line passing through them is
$\frac{y-b}{x-a}=\frac{b-d}{a-c}$
Product of slopes of two perpendicular lines $=-1$
The equation of the line joining points $(2,5)$ and $(-3,6)$ is
$\frac{y-5}{x-2}=\frac{5-6}{2-(-3)}$
or, $\frac{y-5}{x-2}=\frac{-1}{5}$
Or, $5 y-25=-x+2$
i.e. the given line is x + 5y = 27.
The slope of this line is $-1 / 5$.
$\therefore$ the slope of the perpendicular line =
$\frac{-1}{-1 / 5}=5$
The equation of the line can be written in the form y = 5x + c
(c is the y - intercept)
This line passes through ( - 3,5).
Hence, 5 = 5x( - 3) + c or, c = 20
The required equation of the line will be y = 5x + 20
i.e. 5x - y + 20 = 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,