Question:
Find the distance of the point $(3,-5)$ from the line $3 x-4 y=27$
Solution:
Given: Point (3,-5) and line 3x – 4y = 27
To find: The distance of the point $(3,-5)$ from the line $3 x-4 y=27$
Formula used:
We know that the distance between a point P(m,n) and a line ax + by + c = 0 is given by,
$D=\frac{|a m+b n+c|}{\sqrt{a^{2}+b^{2}}}$
The equation of the line is $3 x-4 y-27=0$
Here $m=3$ and $n=-5, a=3, b=-4, c=-27$
$D=\frac{|3(3)-4(-5)-27|}{\sqrt{3^{2}+4^{2}}}$
$D=\frac{|9+20-27|}{\sqrt{9+16}}=\frac{|29-27|}{\sqrt{25}}=\frac{|2|}{5}$
$D=\frac{2}{5}$
The distance of the point $(3,-5)$ from the line $3 x-4 y=27$ is $\frac{2}{5}$ units
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- 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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