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યામભુમિતિ

નીચે આપેલી પ્રત્યેક બિંદુ યુગ્મનાં બિંદુઓ વચ્ચેનું અંતર મેળવો. 
(2, 3), B (7, 9)

Answer

    • નીચે આપેલી પ્રત્યેક બિંદુ યુગ્મનાં બિંદુઓ વચ્ચેનું અંતર મેળવો. 
    (a + b, b - a), (a - b, a + b) 

    Answer
    • bold X bold minusઅક્ષ- પરના બિંદુ bold P નું bold A bold thin space bold left parenthesis bold 11 bold comma bold space bold 12 bold right parenthesis થી અંતર bold 13 એકમ છે. બિંદુ P ના યામ શોધો.
    Answer

    • નીચે આપેલી પ્રત્યેક બિંદુ યુગ્મનાં બિંદુઓ વચ્ચેનું અંતર મેળવો. 
    (-3, 4) (0, 0)

    Answer
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    અંતરસુત્રના ઉપયોગથી બતાવો કે  bold A bold space bold left parenthesis bold 2 bold comma bold space bold 3 bold right parenthesis bold comma bold space bold B bold thin space bold left parenthesis bold 4 bold comma bold space bold 7 bold right parenthesis bold space અને bold C bold space bold left parenthesis bold 0 bold comma bold space bold minus bold space bold 1 bold right parenthesis bold space સમરેખ બિંદુઓ છે. 
    bold A bold space bold left parenthesis bold 2 bold comma bold space bold 3 bold right parenthesis bold comma bold space bold B bold space bold left parenthesis bold 4 bold comma bold space bold 7 bold right parenthesis bold spaceઅને bold C bold space bold left parenthesis bold 0 bold comma bold space bold minus bold space bold 1 bold right parenthesis છે.
    bold AB to the power of bold 2 bold space bold equals bold space bold left parenthesis bold x subscript bold 1 bold space bold minus bold space bold x subscript bold 2 bold right parenthesis to the power of bold 2 bold space bold plus bold space bold left parenthesis bold y subscript bold 1 bold space bold minus bold space bold y subscript bold 2 bold right parenthesis to the power of bold 2 bold space

            bold equals bold space bold left parenthesis bold 2 bold space bold minus bold space bold 4 bold right parenthesis to the power of bold 2 bold space bold plus bold space bold left parenthesis bold 3 bold space bold minus bold space bold 7 bold right parenthesis to the power of bold 2 bold space bold equals bold space bold 4 bold space bold plus bold space bold 16 bold space bold equals bold space bold 20 bold space bold equals bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 5 bold space

    bold therefore bold space bold AB bold space bold equals bold space bold 2 square root of bold 5

    bold BC to the power of bold 2 bold space bold equals bold space bold left parenthesis bold x subscript bold 1 bold space bold minus bold space bold x subscript bold 2 bold right parenthesis to the power of bold 2 bold space bold plus bold space bold left parenthesis bold y subscript bold 1 bold space bold minus bold space bold y subscript bold 2 bold right parenthesis to the power of bold 2
     
          bold equals bold space bold left parenthesis bold 4 bold space bold minus bold space bold 0 bold right parenthesis to the power of bold 2 bold space bold plus bold space bold left parenthesis bold 7 bold space bold minus bold space bold left parenthesis bold minus bold 1 bold right parenthesis bold right parenthesis to the power of bold 2 bold equals bold thin space bold left parenthesis bold 4 bold right parenthesis to the power of bold 2 bold space bold plus bold space bold left parenthesis bold 8 bold right parenthesis to the power of bold 2 bold equals bold space bold 16 bold space bold plus bold space bold 64 bold space bold equals bold space bold 80 bold space bold equals bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 5 bold space

    bold therefore bold space bold BC bold space bold equals bold space bold 4 square root of bold 5

    bold AC to the power of bold 2 bold space bold equals bold space bold left parenthesis bold x subscript bold 1 bold space bold minus bold space bold x subscript bold 2 bold space bold right parenthesis to the power of bold 2 bold space bold plus bold space bold left parenthesis bold y subscript bold 1 bold space bold minus bold space bold y subscript bold 2 bold right parenthesis to the power of bold 2 bold space

           bold equals bold space bold left parenthesis bold 2 bold space bold minus bold space bold 0 bold right parenthesis to the power of bold 2 bold space bold plus bold space bold left parenthesis bold 3 bold space bold minus bold space bold left parenthesis bold minus bold 1 bold right parenthesis bold right parenthesis to the power of bold 2 bold space bold equals bold space bold left parenthesis bold 2 bold right parenthesis to the power of bold 2 bold space bold plus bold space bold left parenthesis bold 4 bold right parenthesis to the power of bold 2 bold equals bold space bold 4 bold space bold plus bold space bold 16 bold space bold equals bold space bold 20 bold space bold equals bold space bold 2 bold space bold cross times bold space bold 2 bold space bold cross times bold space bold 5 bold space

    bold therefore bold space bold AC bold space bold equals bold space bold 2 square root of bold 5

    bold 2 square root of bold 5 bold space bold plus bold space bold 2 square root of bold 5 bold space bold equals bold space bold 4 square root of bold 5 bold space bold AB bold space bold plus bold space bold AC bold space bold equals bold space bold BC bold space bold therefore bold space bold B bold space bold minus bold space bold A bold space bold minus bold space bold C bold space

    bold therefore bold space bold B bold comma bold space bold A bold comma bold space bold space bold C bold spaceસમરેખ બિંદુઓ છે.    
    Answer
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