Question:
Find the area of $\triangle \mathrm{ABC}$ whose vertices are $\mathrm{A}(-3,-5), \mathrm{B}(5,2)$ and $\mathrm{C}(-9,-3)$.
Solution:
Given: The vertices of the triangle are $A(-3,-5), B(5,2)$ and $C(-9,-3)$.
Formula: Area of $\triangle A B C=\frac{1}{2}\left[x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)\right]$
Here,
$x_{1}=-3, y_{1}=-5$
$x_{2}=5, y_{2}=2$
$x_{3}=-9, y_{3}=-3$
Putting the values,
Area of $\triangle \mathrm{ABC}=\frac{1}{2}[-3(2+3)+5(-3+5)-9(-5-2)]$
$=\frac{1}{2}[-15+10+63]$
$=29$ square units.
Therefore, the area of $\triangle \mathrm{ABC}$ is 29 square 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
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- Atoms
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