Geometry Question

Question

A segment can be divided into n congruent segments by bisecting segments repeatedly. What are some of the possible values of​ n? Give a rule for n.

Select all of the choices below that are possible values n.

A. 4

B. 1

C. 2

D. 7

E. 5

F. 8

G. 3

H. 6

Answer 1

If you think about it, when you bisect the original segment, you then have 2 equal segments. Then if you bisect each of those new segments, that gives you 4 segments, then if you bisect each of those segments, you get 8 segments, etc, etc. In other words, if you engage in this bisection repeatedly, then the number of segments increase in the following way: 1, 2, 4, 8, 16, 32, 64, etc. These are all then possible values for n.

You can then create the formula: n = 2*(previous value of n)

In other words each value for n is twice the previous value of n.

Therefore the possible values from the list ar 2, 4 and 8.

Answer 2

Possible values for n: 4(A.); 2 (C.); 8 (F.)

n = 1 also working if not perform bysecting.

So, n = 2^k, k = 0, 1, 2, 3, ...