The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is
A. x – y = 5
B. x + y = 5
C. x + y = 1
D. x – y = 1
B. x + y = 5
Explanation:
Given that straight line passing through the point (3, 2)
And perpendicular to the line y = x
Let the equation of line ‘L’ is
y – y1 = m(x – x1)
Since, L is passing through the point (3, 2)
∴ y – 2 = m(x – 3) … (i)
Now, given eq. is y = x
Since, the above equation is in y = mx + b form
So, the slope of this equation is 1
It is also given that line L and y = x are perpendicular to each other.
We know that, when two lines are perpendicular, then
m1 × m2 = -1
∴ m × 1 = -1
⇒ m = -1
Putting the value of m in equation (i), we get
y – 2 = (-1) (x – 3)
⇒ y – 2 = -x + 3
⇒ x + y = 3 + 2
⇒ x + y = 5
Hence, the correct option is (b)
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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,