question_answer

AOBC is a rectangle whose three vertices area A  (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is

A)  5

B)  3

C)  \[\sqrt{34}\]

D)  4

Correct Answer: C

Solution :

Let the fourth vertex of a rectangle be \[C\,\,({{x}_{1}},{{y}_{1}})\] The length of the diagonal AB = Distance between the points A (0, 3) and B (5, 0) Here,     \[{{x}_{1}}=0,\]\[{{y}_{1}}=3\] and \[{{x}_{2}}=5,\]\[{{y}_{2}}=0\] \[d=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}\] \[=\sqrt{{{(5-0)}^{2}}+{{(0-3)}^{2}}}=\sqrt{25+9}=\sqrt{34}\]