Question

Sa se arate ca triunghiul cu vârfurile A(4,6) B(-2,-2) C(12,0) este isoscel

Answer 1

$AB = \sqrt{( xB - xA)^{2} + {(yB-yA) }^{2} }$

$AB = \sqrt{(-2 -4)^{2} + ( - 2 - 6) ^{2} }$

$AB = \sqrt{ {(-6)}^{2} + {( - 8)}^{2} }$

$AB = \sqrt{36 + 64}$

$AB = \sqrt{100}$

$AB = 10$

$AC = \sqrt{(xC - xA)^{2} + (yC - yA) ^{2} }$

$AC = \sqrt{(12 - 4)^{2} + (0 - 6) ^{2} }$

$AC = \sqrt{ {8}^{2} + ( { - 6)}^{2} }$

$AC = \sqrt{64 + 36}$

$AC = \sqrt{100}$

$AC = 10$

$BC = \sqrt{(xC - xB)^{2} + (yC - yB) ^{2} }$

$BC = \sqrt{(12 + 2)^{2} + (0 + 2) ^{2} }$

$BC = \sqrt{ {14}^{2} + {2}^{2} }$

$BC = \sqrt{196 + 4}$

$BC = \sqrt{200}$

$BC = 10 \sqrt{2}$

$AB=AC \: = > ABC \: triunghi \: isoscel$