Question

Fie un reper cartezian xOy. Aratati ca: Fie punctele A(1,2) B(4,6) C(5,5) sunt varfurile unui triunghi isoscel​

Answer 1

Explicație pas cu pas:

$AB = \sqrt{(x_{B} - x_{A})^{2} + (y_{B} - y_{A})^{2} } = \\ = \sqrt{(4 - 1)^{2} + (6 - 2)^{2} } = \sqrt{3^{2} + 4^{2} }$

$= \sqrt{9 + 16} = \sqrt{25} = 5$

$AC = \sqrt{(x_{C} - x_{A})^{2} + (y_{C} - y_{A})^{2} } = \\ = \sqrt{(5 - 1)^{2} + (5 - 2)^{2} } = \sqrt{4^{2} + 3^{2} }$

$= \sqrt{16 + 9} = \sqrt{25} = 5$

$BC = \sqrt{(x_{C} - x_{B})^{2} + (y_{C} - y_{B})^{2} } = \\ = \sqrt{(5 - 4)^{2} + (5 - 6)^{2} } = \sqrt{1^{2} + ( - 1)^{2} }$

$= \sqrt{1 + 1} = \sqrt{2}$

AB≡AC => triunghi isoscel