Construct a line perpendicular to each given line and through the given point. then explain how do you know the constructed line is perpendicular to the given line

Perpendicular lines is defined in geometry as two lines that intersect or intersect with right angles (90°). The name "perpendicular" comes from the Latin term "perpendiculars," which means "a plumb line."

Some key features regarding the perpendicular lines are-

These lines are always at right angles when they intersect.
When two lines is perpendicular to each other, they are parallel and will never collide.

Now according to the question;

The method of drawing a perpendicular line across a given point includes the following steps:

We will construct an arc from the supplied point R to cut the given line at points A and B.
length RA is now equal as length RB (radius of circle)
currently, with RA length Place the compass on A and B to intersect the arcs to point P on the other side of the specified line. Joining PA and PB now.
The closed RAPB forms a rhombus, and the diagonal bisects it perpendicularly.

To know more about the perpendicular lines, here

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The correct question is-

In the step shown of the construction of a line through a point that is perpendicular to the given line, why must the compass point be placed on points A and B? How would the construction be different if the compass point were placed at random points on the original line?