Students of a school are standing in rows and columns in their school playground to celebrate their

Question

Students of a school are standing in rows and columns in their school playground to celebrate their annual sports day. $A$, $B$, $C$ and $D$ are the positions of four students as shown in the figure.\The figure formed by the four points $A, B, C$ and $D$ is a\

Professor PC Thomas Classes · Answer

(d) : From figure coordinates are $A(2,5), B(5,7)$, $C(8,6)$ and $D(6,3)$.\ Now, $A B=\sqrt{(2-5)^{2}+(5-7)^{2}}=\sqrt{9+4}=\sqrt{13}$ units\ $B C=\sqrt{(5-8)^{2}+(7-6)^{2}}=\sqrt{9+1}=\sqrt{10}$ units\ $C D=\sqrt{(8-6)^{2}+(6-3)^{2}}=\sqrt{4+9}=\sqrt{13}$ units\ $D A=\sqrt{(6-2)^{2}+(3-5)^{2}}=\sqrt{16+4}=\sqrt{20}$ units\ Clearly, $A B C D$ is a quadrilateral