question_answer

If AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B (5, 0), then the length of its diagonal is   

A) 5 units

B) 3 units

C) \[\sqrt{34}\]units

D) A units

Correct Answer: C

Solution :

Now, length of the diagonal AB = Distance between the points A(0, 3) and B(5, 0).

\[\because\]  Distance between the points\[\left( {{x}_{1}},\,{{y}_{1}} \right)\] and \[\left( {{x}_{2}},\,{{y}_{2}} \right)\],

\[d=\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}\]

Here, \[{{x}_{1}}=0,\] \[{{y}_{1}}=3\]and \[{{x}_{2}}=5,\,{{y}_{2}}=0\]

\[\therefore\]  Distance between the points \[A\left( 0,\,3 \right)\]and B (5,0)

\[AB=\sqrt{{{\left( 5-0 \right)}^{2}}+{{\left( 0-3 \right)}^{2}}}\]

\[=\sqrt{25+9}=\sqrt{34}\]

Hence, the required length of its diagonal is  \[\sqrt{34}\] units.