Question:
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
(b) 3
(c) √34
(d) 4
Solution:
Now, length of the diagonal AB = Distance between the points A(0, 3) and B(5, 0).
∴ Distance between the points (x,, y,) and (x2, y2),
$d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$
Here, $x_{1}=0, y_{1}=3$ and $x_{2}=5, y_{2}=0$
$\therefore$ Distance between the points $A(0,3)$ and $B(5,0)$
$A B=\sqrt{(5-0)^{2}+(0-3)^{2}}$
$=\sqrt{25+9}=\sqrt{34}$
Hence, the required length of its diagonal is √34.