Primer 1: data su koordinate temena trougla A(3,2), B(-1,-1) i C(11,-6). Odredi dužine stranica trougla. \( A=(3,2) ,~B=(-1,-1)\\d_{AB}=\sqrt{\left(x_{A}-x_{B} \right)^2+ (y_{A}-y_{B})^2} \)
\( d_{AB}=\sqrt{\left(3-\left( -1\right)\right)^2+ (2-\left(-1 \right) )^2} \)
\[ d_{AB}=\sqrt{\left(3+1\right)^2+\left (2+1\right)^2}=5 \]
\( A=(3,2) ,~C=(11,-6)\\d_{AC}=\sqrt{\left(x_{A}-x_{C} \right)^2+ (y_{A}-y_{C})^2} \)
\( d_{AC}=\sqrt{\left(3-11\right)^2+ (2-\left(-6 \right) )^2} \)
\[ d_{AC}=\sqrt{\left(3-11\right)^2+\left (2+6\right)^2}=\sqrt{128}=8\sqrt{2} \]
\( C=(11,-6) ,~B=(-1,-1)\\d_{CB}=\sqrt{\left(x_{C}-x_{B} \right)^2+ (y_{C}-y_{B})^2} \)
\( d_{CB}=\sqrt{\left(11-\left( -1\right)\right)^2+ (-6-\left(-1 \right) )^2} \)
\( d_{CB}=\sqrt{\left(11+1\right)^2+\left (-6+1\right)^2} \)
\[d_{CB}=\sqrt{144+25}=13 \]
Stranice trougla su AB=5. CB=13 i AC=8\( \sqrt{2} \)