Question

Explain why partitioning a directed line segment into a

ratio of 1:2 is not the same as finding half the length of the
directed line segment.

Answer 1

A ratio of 1:2 means that there are 3 parts in total. One part will be before the desired point, and 2 parts will be after the desired point. This is the same as finding the point that is 1/3 the length. Half the length of the segment would mean there would only be two pieces, each of equal size.

Explanation:

Sample Response...

Answer 2

Explanation:

This is actually a very important question and it is very subtle. Let's just take an ordinary segment.

Suppose we have a segment that is this long

=========o=========

The segment up to the o is nine equal signs long.

The segment after the o is also nine equal signs long.

Here's the crunch. Since they are equal, the ratio is 1 to 1. The segment is divided in half.

Now take the second half of the question.

======o============

The left side of the o is 6 equal signs long.

The right side of the o is 12 equal signs long.

The ratio is 1:2. There are still 18 equal signs but now they are divided as 6/12 which is not the same thing as 9/9

Very interesting question.