Question

when constructing the perpendicular bisector of hk, start by placing the point of the compass at choose... and draw an arc with radius choose... 12 hk.

Answer 1

To construct the perpendicular bisector of segment HK, place the point of the compass at any point on the segment and draw an arc with a radius greater than half the length of segment HK.

Explanation:

Constructing a perpendicular bisector involves finding the midpoint of the segment and drawing a line that intersects it at a 90-degree angle. To begin, place the compass's point anywhere on segment HK and draw two arcs of equal radius greater than half the length of HK. This action ensures the arcs intersect at two points, providing us with a sufficient reference for the midpoint of HK. Label these intersection points as A and B. Then, use a straightedge to draw a line passing through points A and B, extending it beyond the segment. This line is the perpendicular bisector of segment HK.

The reasoning behind using a radius greater than half the length of HK is to ensure the arcs intersect at two distinct points. If the radius were less than half, the arcs would either not intersect or intersect at the endpoints, preventing the accurate identification of the segment's midpoint. The perpendicular bisector ensures that any point on the line is equidistant from the endpoints of the segment, forming right angles at the midpoint. Therefore, by using this construction method, we can confidently establish the perpendicular bisector of segment HK.

Answer 2

To construct a perpendicular bisector of a segment HK, place the compass at the endpoints H or K and draw arcs with a radius greater than half of HK's length. The perpendicular bisector is the line connecting the intersection points of these arcs.

Step-by-step explanation:

To construct the perpendicular bisector of a line segment HK, you need to place the point of the compass at either endpoint of the segment (H or K) and draw an arc that intersects the line above and below it. The radius of the arc should be more than half the length of the line segment to ensure the arcs intersect when drawn from both endpoints. The intersection points of the arcs, when connected, give you the line that is the perpendicular bisector of HK. This line will be equidistant from the endpoints H and K and will intersect HK at a 90-degree angle.

If HK is 12 units long, then the radius of your arcs should be more than 6 units to ensure that the arcs intersect. Assuming the length of HK is known, the compass radius should be set to any length greater than half of HK's length but less than the full length (for practicality and ease of drawing), such as 9 units, if we follow the provided example.

Remember, accurate construction involves careful measurements with the compass and straightedge (or ruler), and the process can be repeated to increase precision.