Q: Why x axis and y axis must be perpendicular to each other?

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Not always because the diagonals of a rectangle bisect each other but they are not perpendicular to each other.

It is a rhombus

no

With a compass and a straight edge and the lines must bisect each other at 90 degrees

It is impossible for parallel lines to be perpendicular. Perpendicular lines are intersecting lines, meaning that they cross each other. Parallel lines, on the other hand, are lines that never meet, no matter how far they are extended in either direction. So intersecting lines (which includes perpendicular lines) and parallel lines are exact opposites. Parallel lines will never meet or cross; they cannot be perpendicular.

Related questions

Not always because the diagonals of a rectangle bisect each other but they are not perpendicular to each other.

False

false

It is a rhombus

no

The perpendicular axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two perpendicular axes lying in the plane of the object and intersecting the first axis. This theorem can be proven using the parallel axis theorem and considering the individual moments of inertia about each axis. The perpendicular axis theorem is commonly used to find the moment of inertia of thin planar objects.

The slopes of two perpendicular lines are negative inverses of each other. In other words, the two slopes when multiplied together equal -1.

With a compass and a straight edge and the lines must bisect each other at 90 degrees

In physics, the perpendicular axis theorem (or plane figure theorem) can be used to determine the moment of inertia of a rigid object that lies entirely within a plane, about an axis perpendicular to the plane, given the moments of inertia of the object about two perpendicular axes lying within the plane. The axes must all pass through a single point in the plane.Define perpendicular axes , , and (which meet at origin ) so that the body lies in the plane, and the axis is perpendicular to the plane of the body. Let Ix, Iy and Iz be moments of inertia about axis x, y, z respectively, the perpendicular axis theorem states that[1]This rule can be applied with the parallel axis theorem and the stretch rule to find moments of inertia for a variety of shapes.If a planar object (or prism, by the stretch rule) has rotational symmetry such that and are equal, then the perpendicular axes theorem provides the useful relationship:

It is impossible for parallel lines to be perpendicular. Perpendicular lines are intersecting lines, meaning that they cross each other. Parallel lines, on the other hand, are lines that never meet, no matter how far they are extended in either direction. So intersecting lines (which includes perpendicular lines) and parallel lines are exact opposites. Parallel lines will never meet or cross; they cannot be perpendicular.

You could prove this by congruent triangles, but here are two simpler arguments: --------------- Since a square is a rhombus, and the diagonals of a rhombus are perpendicular bisectors of each other, then the diagonals of a square must be perpendicular bisectors of each other -------------------- A square has four-fold rotational symmetry - as you rotate it around the point where the diagonals cross, there are four positions in which it looks the same. This means that the four angles at the centre must be equal. They will each measure 360/4 = 90 degrees, so the diagonals are perpendicular. Also. the four segments joining the centre to a vertex are all equal, so the diagonals bisect each other.

False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.