The x and y axis need to be perpendicular to each other in order for them to intersect each other at the point of origin (0, 0) on the Cartesian plane,
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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.