Show that the length of the perpendicular from the point (7, 0) to the line 5x + 12y – 9 = 0 is double the length of perpendicular to it from the point (2, 1)
Given: Points (7,0) and (2,1) , line 5x + 12y – 9 = 0
To Prove : length of the perpendicular from the point $(7,0)$ to the line $5 x+12 y-9=0$ is double the length of perpendicular to it from the point $(2,1)$
Formula used: We know that the length of the perpendicular from $(\mathrm{m}, \mathrm{n})$ to the line $\mathrm{ax}+$ by $+c=0$ is given by,
$D=\frac{|a m+b n+c|}{\sqrt{a^{2}+b^{2}}}$
Let $D_{1}$ be the length of perpendicular from the point $(7,0)$ to the line $5 x+12 y-9=0$
The given equation of the line is $5 x+12 y-9=0$
Here at point $(7,0) \mathrm{m}=7$ and $\mathrm{n}=0, \mathrm{a}=5, \mathrm{~b}=12, \mathrm{c}=-9$
$D_{1}=\frac{|5(7)+12(0)-9|}{\sqrt{5^{2}+12^{2}}}$
$D_{1}=\frac{|35+0-9|}{\sqrt{25+144}}=\frac{26}{\sqrt{169}}=\frac{26}{13}=2$
$D_{1}=2$
Let $D_{2}$ be the length of perpendicular from the point $(2,1)$ to the line $5 x+12 y-9=0$
The given equation of the line is $5 x+12 y-9=0$
Here at point $(2,1) m=2$ and $n=1, a=5, b=12, c=-9$
$D_{2}=\frac{|5(2)+12(1)-9|}{\sqrt{5^{2}+12^{2}}}$
$D_{2}=\frac{|10+12-9|}{\sqrt{25+144}}=\frac{22-9}{\sqrt{169}}=\frac{13}{13}=1$
$D_{2}=1$
$D_{1}=2 D_{2}=2$
Thus the length of the perpendicular from the point $(7,0)$ to the line $5 x+12 y-9=0$ is double the length of perpendicular to it from the point $(2,1)$
- 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,
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,