Question

Question 5
If AOBC is a rectangle whose three vertices are A(0,3), 0(0,0) and B(5,0), then the length of its diagonal is:
(A) 5
(B) 3
(C) $\sqrt{34}$
(D) 4

Answer 1

Now, length of the diagonal AB = Distance between the points A(0,3) and B(5,0)
$\because \text{Distance between the points}(x_1,y_1)and(x_2,y_2),d=\sqrt{(x_2-x_2{)}^2+(y_2-y_2{)}^2}$
Here, $x_1=0,y_1=3and{x}_2=5,y_2=0$
$\therefore$ Distance between points (0,3) and (5,0)
$AB=\sqrt{(5-0{)}^2+(0-3{)}^2}$
$=\sqrt{25+9}=\sqrt{34}$
Hence, the required length of its diagonal is $\sqrt{34}$.