Question

1 n.b: you need a compass and a straightedge. a) draw segment ab. b) draw perpendicular bisector of segment ab. c) take point p on the perpendicular bisector of ab. to which is the point p closer to?

Explanation:

Step1: Draw segment AB

Use a straight - edge to draw a line segment connecting points A and B.

Step2: Draw perpendicular bisector of segment AB

1. Place the compass at point A and set the radius to be more than half of the length of AB. Draw arcs above and below the segment AB.
2. Without changing the compass width, place the compass at point B and draw similar arcs that intersect the previous arcs.
3. Use the straight - edge to draw a line through the intersection points of the arcs. This is the perpendicular bisector of AB.

Step3: Analyze the distance of point P

By the property of the perpendicular bisector of a line segment, any point on the perpendicular bisector of a line segment is equidistant from the endpoints of the line segment. So, if point P is on the perpendicular bisector of AB, the distance from P to A is equal to the distance from P to B.

Answer:

Point P is equidistant from A and B.