Question

1. When bisecting a line segment, why must you find the intersection points of the arcs both above and below the line segment? A. To make sure that you get a straight line to bisect the line segment. B. The intersection point above the line segment overestimates the midpoint, while the intersection point below the line segment underestimates the midpoint. C. Finding both intersection points helps if the line segment is not completely vertical or horizontal. D. Only one intersection point is needed to find the midpoint, but finding both points allows you to check your work. 2. A line segment has a length of approximately 10 cm. If a compass is set to a width of 9 cm, will it still be possible to bisect the line segment? Explain. A. No, it is not possible. The compass should be just a little bit wider than half of the length of the line segment, which in this case is 5 cm. B. Yes, it is still possible. The width of the compass in respect to the length of the line segment does not matter. C. No, it is not possible. The width of the compass should be exactly half of the length of the line segment, which in this case is 5 cm. D. Yes, it is still possible. So long as the compass is wider than half the length of the line segment and still intersects the line segment, it is possible to bisect the line segment.

Answer 1

A)Option A - To make sure that you get a straight line to bisect the line segment

B) Option D - Yes, it is still possible. So long as the compass is wider than half the length of the line segment and still intersects the line segment, it is possible to bisect the line segment.

Explanation:

1) In bisection of a line segment, we seek to divide the line into 2 equal parts. Now, when using the bisection points of an arc, it's important to have two intersection points above and below the line segment so that we can draw a straight line that will pass through the horizontal line segment we are bisecting to make the bisected parts equal in length.

So option A is correct.

2) When bisecting a horizontal line segment using compass, usually we place one leg of the compass at one endpoint of the line and open the other leg of the compass to a length that's more than half of the horizontal line segment. Thereafter, we draw our arc from top to bottom. Without changing the distance of the opened compass, we put one of the legs at the 2nd endpoint and now draw another arc to intersect the previously drawn one.

Now, from the question we are told that the line segment has a length of approximately 10 cm and the compass is set to a width of 9 cm. Now, since 9cm is more than half of the line segment and provided this width of 9cm is maintained when moving the leg to the second endpoint, then it is possible.

Option D is correct.