The point of intersection of the diagonals of | vedclass

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(A) The diagonals of a square bisect each other at $90^{\circ}$ at the origin. Let the vertices be on the axes. The distance from the origin to each v

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The diagonals of a square bisect each other at $90^{\circ}$ at the origin. Let the vertices be on the axes. The distance from the origin to each vertex is half the length of the diagonal.Since the side length is $a$,the diagonal length $d$ is given by $d = a\sqrt{2}$.The distance from the origin to each vertex is $\frac{d}{2} = \frac{a\sqrt{2}}{2} = \frac{a}{\sqrt{2}}$.Thus,the vertices of the square are $\left(\frac{a}{\sqrt{2}}, 0\right)$,$\left(-\frac{a}{\sqrt{2}}, 0\right)$,$\left(0, \frac{a}{\sqrt{2}}\right)$,and $\left(0, -\frac{a}{\sqrt{2}}\right)$.Comparing these with the given options,the point $(a\sqrt{2}, 0)$ is not a vertex of the square.

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 $a$,then which of the following is $NOT$ a vertex of the square?

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