Question

Fie A(1;3) B(-2;5) C(3;-1)
Reprezinta punctele intr.un reper XoY
Calculeaza perimetrul triunghiului ABC

Answer 1

$AB= \sqrt{(X _{A}-X _{B} ) ^{2} +(Y _{A} -Y _{B}) ^{2} } = \sqrt{(1+2) ^{2} +(3-5) ^{2} } = \sqrt{9+4}$
=>AB=√13
$AC= \sqrt{(X _{A}-X _{C} ) ^{2}+(Y _{A} -Y _{C}) ^{2} } = \sqrt{(1-3) ^{2}+(3+1) ^{2} } = \sqrt{4+16}$
=>AC=2√5
$BC= \sqrt{(X _{B-X _{C} }) ^{2} +(Y _{B}-Y _{C}) ^{2} }= \sqrt{(-2-3) ^{2}+(5+1)^{2} }$
=>BC=√61
=>P=√13+2√5+√61√