The length of the diagonal of rectangle ABCD formed by A(2,-2), B(8,4), C(5,7) and D(-1,1) is
$3 \sqrt{10}$
$2 \sqrt{10}$
$\sqrt{85}$
$\sqrt{80}$

Question

The length of the diagonal of rectangle ABCD formed by A-2-2- B-8-4- C-5-7- and D-1-1- isdisplaystyle 3sqrt-10-displaystyle 2sqrt-10-displaystyle sqrt-85-displaystyle sqrt-80-

Toppr Admin · Accepted Answer

AC-x221A-2-x2212-5-2-x2212-2-x2212-7-2-x221A-9-81-x221A-90-3-x221A-10

The length of the diagonal of rectangle ABCD formed by A(2,-2), B(8,4), C(5,7) and D(-1,1) is3√102√10√85√80

AC=√(2−5)2+(−2−7)2=√9+81=√90=3√10

The length of the diagonal of rectangle ABCD formed by A(2,-2), B(8,4), C(5,7) and D(-1,1) is
$3 \sqrt{10}$
$2 \sqrt{10}$
$\sqrt{85}$
$\sqrt{80}$

$A C = \sqrt{{(2 - 5)}^{2} + {(- 2 - 7)}^{2}} = \sqrt{9 + 81} = \sqrt{90} = 3 \sqrt{10}$