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Analytical Geometry

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13 Sep 2009 20:02:25 IST

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IIT QUESTION!!!! the total number of integral coordinate points that lie exactly inside t,

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IIT QUESTION!!!! the total number of integral points that lie exactly inside triangle formed by points (0,0) (4,0) (0,4) are????

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eragon24

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13 Sep 2009 20:08:15 IST

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ek triangle banao with given cordinates fir uske andar jitney bhi integral points aa rahey hain unhe count karlo.....

Vivek Agrawal

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13 Sep 2009 20:15:51 IST

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lolz answer is 190

C!-!!NMAY

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13 Sep 2009 20:18:09 IST

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answer phir se check karo...

Vivek Agrawal

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13 Sep 2009 20:21:56 IST

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oye hoye ye maine thora sa data galat de diya :D :Pcoridinate of vertices are (0,0) (21,0) and (0,21)

Vivek Agrawal

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13 Sep 2009 20:30:38 IST

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are kal cpt hai koi to jaldi se jabawab do ....mai jayda der tak pc par nahi reh sakta padhai bhi karni hai

Vivek Agrawal

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13 Sep 2009 20:31:33 IST

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kal mera birthday bhi hai and cpt bhi...hmmm...cpt ne birthday ka maja kirkira kar diya yaar :(( damn narayna and its cpt :P

Vivek Agrawal

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13 Sep 2009 20:43:30 IST

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are koi to jawab do

Hari Shankar

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13 Sep 2009 20:50:29 IST

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I doubt if this is an IIT question.

This is an application of what is known as Pick's Theorem:

If a simple polygon has its vertices as lattice points (what you are referring to as integer points), suppose there are p lattice points on its boundary and q in the interior, then the area of the polygon is given by q + p/2 - 1.

There are 63 points on the boundary and area is 441/2, so the number of points is 190

AJAY CHANDRASHEKAR

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13 Sep 2009 20:52:14 IST

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ITS A SIMPLE ONE

TOTAL NO. OF POINTS WITH INTERAL CO ORDINATES= (21(21+1))/2 =231

THERE ARE TOTAL 41 POINTS WITH INTEGRAL CODINATES AT THE BOUNDRY HENCE SUBTRACTING WE GET 190

Vivek Agrawal

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13 Sep 2009 20:53:50 IST

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ye iit ka hi question hai sir.....IIT 2003 3 screening paperarihant me pg no 90 q no 14 me diya hai and answer bhi 190 hi diya hai sir

Vivek Agrawal

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13 Sep 2009 20:54:59 IST

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@ AJAY CHANDERSHEKHAR ye kaise hua bhai samjha nahi

AJAY CHANDRASHEKAR

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13 Sep 2009 20:55:43 IST

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IIT QUESTION!!!! the total number of integral coordinate points that lie exactly inside t,

Hari Shankar

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13 Sep 2009 20:56:05 IST

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sry, calc mistake. 190 is right

AJAY CHANDRASHEKAR

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13 Sep 2009 20:58:40 IST

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SEE THERE ARE 21(INTEGRAL CO ORDINATES) POINTS IN BOTTOM LINE AS WE MOVE UP IT DECREACES BY 1 AND AT THE END WE GET 1 POINT .SO ADDING ALL USING FORMULA OF SUM OF FIRST N NATURAL NUMBERS WE GET 231 AND BOUNDRY POINTS ARE 21+21-1(ORIGIN IS COMMON FOR BOTH)

Vivek Agrawal

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13 Sep 2009 21:02:20 IST

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wah thanks bhai mai bhi isi tarah ap me soch raha tha bas 231 tak la kar ruk jaa raha tha aour 41 nahi ghata raha tha....now i understood ....thx a lot rated u

Vivek Agrawal

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13 Sep 2009 21:11:27 IST

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@ ajay bropatnai am in 11thhere in patna maths faculty(mr.kushal mahataley)is fantastic really awesome...but chem and phy faculty are not good...however i can manage chemistry but phy!hmmmm....i dont know wat to do...i can be amongst top 3 in every cpt but due to phy i hv to be satisfied with 10-20 rank each time coz in phy each time less than 20 marks in odrs 50+ especially maths which take my rank high.....

AJAY CHANDRASHEKAR

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13 Sep 2009 21:15:25 IST

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refer to theory books by dc pandey..they are really awesome..do many solved examples and solve hcv complety...even narayana's new packages are good

Vivek Agrawal

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13 Sep 2009 21:37:35 IST

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bro yehi to problem hai arihant le li hai...theory to samjah me aa jati hai concepts bhi crystal clear ho jaate hain but when it comes to numericals then APPLY nahi kar pata hoon...coaching ke sir me bhi yehi problem hai ki wo thoery to bahut deep padhate hain lekin application nahi sikhate hain :(

Nizam Siddiqui

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13 Sep 2009 21:42:41 IST

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use concept of permutation and combination ....

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