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યામભુમિતિ

જે રેખા ખંડનાં અંત્યબિંદુઓ A(3, -2) અને B(-1, 4) હોય, તે રેખાખંડના મધ્યબિંદુના યામ શોધો.

અહીં, A(x₁, y₁) = A(3, -2)

અને B(x₂, y₂) = B(-1, 4) છે.

$top enclose bold AB bold space bold ન ા bold space bold મધ ્ યબ િં દ ુ ન ા bold space bold ય ા bold equals bold space open parentheses fraction numerator bold x subscript bold 1 bold space bold plus bold space bold x subscript bold 2 over denominator bold 2 end fraction bold comma fraction numerator bold y subscript bold 1 bold space bold plus bold space bold y subscript bold 2 over denominator bold 2 end fraction close parentheses bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold space open parentheses fraction numerator bold 3 bold space bold plus bold space bold left parenthesis bold minus bold 1 bold right parenthesis over denominator bold 2 end fraction bold comma fraction numerator bold minus bold 2 bold space bold plus bold space bold 4 over denominator bold 2 end fraction close parentheses bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold equals bold left parenthesis bold 1 bold comma bold space bold 1 bold right parenthesis$

આમ, $top enclose bold AB$ ના મધ્યબિંદુના યામ (1, 1) છે.

D(3, 2), E(5, 6) અને F(-1, 7) અનુક્રમે ABC ની બાજુઓ $top enclose bold BC bold comma bold space top enclose bold CA bold comma bold space bold અન ે bold space top enclose bold AB$ નાં મધ્ય બિંદુઓ છે. A, B અને Cના યામ શોધો.

સાબિત કરો કે, બિંદુઓ A(3, 2), B(5, 8) અને C(-6, 5) એ કાટકોણ ત્રિકોણનાંં શિરોબિંદુઓ છે.

બિંદુઓ A(2, 3) અને B(-3, -9) વચ્ચેનું અંતર શોધો.

સાબિત કરો કે, P(2, -1), Q(1, -4) અને R(3, 2) સમરેખ બિંદુઓ છે.

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