The point of intersection of the diagonals of | vedclass

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(A) Let the vertices of the square be $A, B, C,$ and $D$. Since the diagonals lie along the coordinate axes and the side length is $a$,the distance fr

Vedclass · Accepted Answer

$(a\sqrt{2}, 0)$

Vedclass · Answer

(A) Let the vertices of the square be $A, B, C,$ and $D$. Since the diagonals lie along the coordinate axes and the side length is $a$,the distance from the origin to each vertex is half the length of the diagonal.The diagonal length $d$ of a square with side $a$ is $a\sqrt{2}$.Thus,the distance from the origin to each vertex is $\frac{a\sqrt{2}}{2} = \frac{a}{\sqrt{2}}$.The vertices are located at $(\frac{a}{\sqrt{2}}, 0), (0, \frac{a}{\sqrt{2}}), (-\frac{a}{\sqrt{2}}, 0),$ and $(0, -\frac{a}{\sqrt{2}})$.Comparing these with the given options,$(a\sqrt{2}, 0)$ is not a vertex.

The point of intersection of the diagonals of a square is at the origin,and the coordinate axes are drawn along the diagonals. If the side length of the square is $a$,which of the following is $NOT$ a vertex of the square?

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