Question:
Two vertices of a triangle ABC are A(2, -4, 3) and B(3, -1, -2), and its centroid is (1, 0, 3). Find its third vertex C.
Solution:
Since the centroid of a triangle
$=\left(\frac{x_{2}+x_{1}+x_{1}}{3}, \frac{y_{2}+y_{1}+y_{2}}{3}, \frac{z_{2}+z_{1}+z_{3}}{3}\right)$
The points are $A(2,-4,3)$ and $B(3,-1,-2)$, and its centroid is $(1,0,3)$. And let its third vertex $\mathrm{C}(\mathrm{a}, \mathrm{b}, \mathrm{c})$
Using the formula, we get
$=\left(\frac{2+3+a}{3}, \frac{-4-1+b}{3}, \frac{3-1+c}{3}\right)$
$=\left(\frac{5+a}{3}, \frac{-5+b}{3}, \frac{2+c}{3}\right)$
Equating it with the coordinates of centroid, we get
$1=\frac{5+a}{3}$
$a=-2$
$0=\frac{-5+b}{3}$
$b=-5$
and,
$\frac{2+c}{3}=3$
c = 7
therefore, the point is $(-2,-5,7)$
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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
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- Dual Nature of Radiation and Matter
- Atoms
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- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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