$A O B C$ is a rectangle whose three vertices are $A(0,2), O(0,0)$ and $B(4,0)$. The square of the l

Question

$A O B C$ is a rectangle whose three vertices are $A(0,2), O(0,0)$ and $B(4,0)$. The square of the length of its diagonal is equal to :\

Professor PC Thomas Classes · Answer

(b) : In rectangle $A O B C, A B$ is the diagonal, where $A(0,2)$ and $B(4,0)$.\ $$ \begin{aligned} & A B=\sqrt{(4-0)^{2}+(0-2)^{2}}=\sqrt{(4)^{2}+(-2)^{2}}=\sqrt{16+4}=\sqrt{20} \ & \Rightarrow(A B)^{2}=20 \end{aligned} $$ Concept Applied - Distance between two points $P\left(x_{1}, y_{1}ight)$ and $Q\left(x_{2}, y_{2}ight)$ is given by $P Q=\sqrt{\left(x_{2}-x_{1}ight)^{2}+\left(y_{2}-y_{1}ight)^{2}}$