Chapter 1.1, Problem 48E

To determine

To find: if the given statement is true or false.

Answer to Problem 48E

False

Explanation of Solution

Given:

Statement: “To divide a line segment into 16 parts, midpoint formula needs to be applied 16 times.”

Concept Used:

Midpoint Formula: Midpoint of the line segment joining the two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by:

  $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Midpoint formula is used to divide a line segment joining two points in two equal parts.

So, to divide line in two equal parts, midpoint formula is applied once. Now apply midpoint formula to each of the two equal parts obtained above to obtain 4 equal parts. That is, using midpoint formula three times $\left(1+2=3\right)$ , to obtain four equal parts.

Now again apply midpoint formula to each of the four equal parts obtained above to obtain 8 equal parts. That is, using midpoint formula total seven times $\left(3+4=7\right)$ , eight equal parts are obtained.

Now again apply midpoint formula to each of the 8 equal parts obtained above to obtain 16 equal parts. That is, using midpoint formula total 15 times $\left(7+8=15\right)$ , 16 equal parts are obtained.

Conclusion:

Given statement that to divide a line segment into 16 parts, midpoint formula needs to be applied 16 times is false because it needs to be applied 15 times only.