Draw the graphs of x − y + 1 = 0 and 3x + 2y − 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and x-axis and shade the triangular area. Calculate the area bounded by these lines and x-axis.
The given equations are
$x-y+1=0$...$.(i )$
$3 x+2 y-12=0$$...(i i)$
Putting $x=0$ in equation $(i)$, we get:
$\Rightarrow 0-y=-1$
$\Rightarrow y=1$
$x=0, \quad y=1$
Putting $y=0$ in equation (i) we get:
$\Rightarrow x-0=-1$
$\Rightarrow x=-1$
$x=-1, \quad y=0$
Use the following table to draw the graph.
Draw the graph by plotting the two points $A(0,1), B(-1,0)$ from table.
$3 x+2 y=12$....(ii)
Putting $x=0$ in equation (ii) we get:
$\Rightarrow 3 \times 0+2 y=12$
$\Rightarrow y=6$
$x=0, \quad y=6$
Putting $y=0$ in equation $(i i)$. We get:
$\Rightarrow 3 x+2 \times 0=12$
$\Rightarrow x=4$
$x=4, \quad y=0$
Use the following table to draw the graph.
Draw the graph by plotting the two points $C(0,6), D(4,0)$ from table.
The two lines intersect at $P(2,3)$.
Now, Required area = Area of shaded region
$\Rightarrow$ Required area $=$ Area of PBD
$\Rightarrow$ Required area $=1 / 2$ (basexheight)
$\Rightarrow$ Required area $=1 / 2(B D \times P M)$
$\Rightarrow$ Required area $=1 / 2(5 \times 3)$ sq. units
Hence the area $=7.5$ sq.units
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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,