Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

JEE Class main Answered

D,E and F are the midpoints of sides BC,CA and AB respetiely of triangle ABC and G is the centroid of the triangle,then GD+GE+GF=
Asked by g_archanasharma | 15 Apr, 2019, 05:51: PM
answered-by-expert Expert Answer
L e t space A left parenthesis x subscript 1 comma y subscript 1 right parenthesis comma space B left parenthesis x subscript 2 comma y subscript 2 right parenthesis space a n d space C left parenthesis x subscript 3 comma y subscript 3 right parenthesis space b e space t h e space c o o r d i n a t e s space o f space v e r t i c e s space o f space t r i a n g l e space A B C G space i s space t h e space c e n t r o i d comma space t h e n G equals open parentheses fraction numerator x subscript 1 plus x subscript 2 plus x subscript 3 over denominator 3 end fraction comma fraction numerator y subscript 1 plus y subscript 2 plus y subscript 3 over denominator 3 end fraction close parentheses A l s o comma space D equals open parentheses fraction numerator x subscript 2 plus x subscript 3 over denominator 2 end fraction comma fraction numerator y subscript 2 plus y subscript 3 over denominator 2 end fraction close parentheses comma space E equals open parentheses fraction numerator x subscript 1 plus x subscript 3 over denominator 2 end fraction comma fraction numerator y subscript 1 plus y subscript 3 over denominator 2 end fraction close parentheses space a n d space F open parentheses fraction numerator x subscript 1 plus x subscript 2 over denominator 2 end fraction comma fraction numerator y subscript 1 plus y subscript 2 over denominator 2 end fraction close parentheses N o w comma space G D equals square root of open parentheses fraction numerator x subscript 2 plus x subscript 3 over denominator 2 end fraction minus fraction numerator x subscript 1 plus x subscript 2 plus x subscript 3 over denominator 3 end fraction close parentheses squared plus open parentheses fraction numerator y subscript 2 plus y subscript 3 over denominator 2 end fraction minus fraction numerator y subscript 1 plus y subscript 2 plus y subscript 3 over denominator 3 end fraction close parentheses squared end root space space space space space space space space space space space space space space equals square root of open parentheses fraction numerator x subscript 2 plus x subscript 3 minus 2 x subscript 1 over denominator 6 end fraction close parentheses squared plus open parentheses fraction numerator y subscript 2 plus y subscript 3 minus 2 y subscript 1 over denominator 6 end fraction close parentheses squared end root S i m i l a r l y comma space G E equals square root of open parentheses fraction numerator x subscript 1 plus x subscript 3 minus 2 x subscript 2 over denominator 6 end fraction close parentheses squared plus open parentheses fraction numerator y subscript 1 plus y subscript 3 minus 2 y subscript 2 over denominator 6 end fraction close parentheses squared end root space a n d space G F equals square root of open parentheses fraction numerator x subscript 1 plus x subscript 2 minus 2 x subscript 3 over denominator 6 end fraction close parentheses squared plus open parentheses fraction numerator y subscript 1 plus y subscript 2 minus 2 y subscript 3 over denominator 6 end fraction close parentheses squared end root S o space w e space h a v e G D plus G E plus G F equals square root of open parentheses fraction numerator x subscript 2 plus x subscript 3 minus 2 x subscript 1 over denominator 6 end fraction close parentheses squared plus open parentheses fraction numerator y subscript 2 plus y subscript 3 minus 2 y subscript 1 over denominator 6 end fraction close parentheses squared end root plus square root of open parentheses fraction numerator x subscript 1 plus x subscript 3 minus 2 x subscript 2 over denominator 6 end fraction close parentheses squared plus open parentheses fraction numerator y subscript 1 plus y subscript 3 minus 2 y subscript 2 over denominator 6 end fraction close parentheses squared end root plus square root of open parentheses fraction numerator x subscript 1 plus x subscript 2 minus 2 x subscript 3 over denominator 6 end fraction close parentheses squared plus open parentheses fraction numerator y subscript 1 plus y subscript 2 minus 2 y subscript 3 over denominator 6 end fraction close parentheses squared end root space space space space space space space space space space space space space space space space space space space space space space equals 1 over 6 open parentheses square root of open parentheses x subscript 2 plus x subscript 3 minus 2 x subscript 1 close parentheses squared plus open parentheses y subscript 2 plus y subscript 3 minus 2 y subscript 1 close parentheses squared end root space plus square root of open parentheses x subscript 1 plus x subscript 3 minus 2 x subscript 2 close parentheses squared plus open parentheses y subscript 1 plus y subscript 3 minus 2 y subscript 2 close parentheses squared end root space plus square root of open parentheses x subscript 1 plus x subscript 2 minus 2 x subscript 3 close parentheses squared plus open parentheses y subscript 1 plus y subscript 2 minus 2 y subscript 3 close parentheses squared end root space close parentheses
Answered by Renu Varma | 16 Apr, 2019, 09:58: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
JEE main - Maths
solution please
question image
Asked by piyurawriya | 24 Apr, 2024, 12:46: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
answer
question image
Asked by piyurawriya | 23 Apr, 2024, 02:02: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
let M be the skew symmetric orthogonal real matrix.Then only possible eigen values are
Asked by kakumanumanoj282 | 20 Apr, 2024, 06:07: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
sin-1(sin5π/3)
Asked by nirmalraulji5 | 18 Apr, 2024, 09:03: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
1
question image
Asked by hadiabbas803 | 17 Apr, 2024, 07:36: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
Cos66+sin84
Asked by veerababukoppisettiveerababu3 | 17 Apr, 2024, 05:49: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
how to solve this in financial calculator by log
question image
Asked by usakoyalshailesh | 15 Apr, 2024, 09:48: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
dout
question image
Asked by satnamk123 | 15 Apr, 2024, 01:50: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
I am not able to get the idea for solving this question I know properties of det.
question image
Asked by sharmalalita847 | 14 Apr, 2024, 09:21: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
A∆B=AUB/A'UB'
Asked by sarthakshukla7275 | 14 Apr, 2024, 01:29: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×