Find the area of the triangle formed by the lines x = 0, y = 1 and 2x + y = 2.
The given equations are
$x=0 \ldots(\mathrm{i})$
$y=1 \ldots(\mathrm{ii})$
and $2 x+y=2 \ldots$ (iii)
Let eq. (i), (ii) and (iii) represents the sides AB, BC and AC respectively of ΔABC
From eq. (i) and (ii), we get $x=0$ and $y=1$
Thus, $A B$ and $B C$ intersect at $(0,1)$
Solving eq. (ii) and (iii), we get
$y=1 \ldots$ (ii)
and $2 x+y=2 \ldots$ (iii)
Putting the value of y = 1 in eq. (iii), we get
$2 x+1=2$
$\Rightarrow 2 x=1$
$\Rightarrow x=\frac{1}{2}$
Thus, $\mathrm{BC}$ and $\mathrm{AC}$ intersect at $\left(\frac{1}{2}, 1\right)$
Now, Solving eq. (iii) and (i), we get
$2 x+y=2 \ldots$ (iii)
and $x=0 \ldots$ (i)
Putting the value of x = 0 in eq. (iii), we get
y = 2
Thus, AC and AB intersect at (0, 2)
So, vertices of triangle $\mathrm{ABC}$ are : $(0,1),\left(\frac{1}{2}, 1\right)$ and $(0,2)$
$\therefore$ Area of $\triangle \mathrm{ABC}=\frac{1}{2} \times$ base $\times$ height
$=\frac{1}{2} \times \frac{1}{2} \times 1$
$=\frac{1}{4} \mathrm{sq} .$ 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,