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Isosceles Triangle Area

The points $A\, (5,-5)$ and $B\, (-1,-1)$ are the endpoints of the hypotenuse of an isosceles right triangle $\triangle ABC$ . What is the area of $ABC$ ?

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$\frac{a}{b}$
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$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

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$\infty$

The length of the hypotenuse is given by the distance formula to be

$\sqrt{(5-(-1))^2 + (-5-(-1))^2} = \sqrt{6^2+4^2} = \sqrt{52}$ . The length of the leg is then given by

$\sqrt{52}/\sqrt{2} = \sqrt{26}$ (alternatively, the Pythagorean Theorem can be applied), and the area of the isosceles right triangle is then equal to

$\frac 12 \cdot \sqrt{26} \cdot \sqrt{26} = \boxed{13}$ .

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