Question

shanti wants to draw a line through point p, which is perpendicular to the line segment qr shown in the figure. she has already positioned her compass point on the intersection m and setting the compass distance equal to that between the intersection m and she can draw another circle that can be used to draw her line. at which point should shanti place her compass if this point represents the center of the new circle used in the construction? at point q at point p at intersection m at intersection n

Explanation:

Step1: Recall perpendicular - line construction

To draw a line through point $P$ perpendicular to line segment $QR$, we use the property of circles in geometric construction. After some initial steps (not fully described here but related to the intersection $m$), the next step is to place the compass at point $P$. When we place the compass at point $P$ and set the appropriate radius (equal to the distance related to the previous construction steps), we can draw a circle that will help in finding the perpendicular line.

Answer:

B. at point $P$