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.

The half -length of the directed line segment is  as the length of the directed line segment is divided into the ratio of .

Further explanation:

Ratio is the quantitative relation or comparison between two different objects or things.

Given:

It is given that a directed line segment is divided in the ratio of .

Step by step explanation:

Step 1

The directed line segment is divided in the ratio of .

It means that there are total 3 parts as it includes three pieces.

One part is before the required point and 2 parts are after the required point.

Step 2:

The half-length of the directed line segment means there is only two parts of equal size.

Step 3:

Consider an example a ribbon has length of 6cm.

Now divide the ribbon into the ratio of .

Therefore, the ribbon is partitioned in the ratio of  as  

Now divide the ribbon equally that is half of the ribbon.

Therefore, the ribbon is partitioned into half as .

Thus, it has been proved the given explanation.

Learn more:  

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Trigonometry

Keywords: directed, line segment, length, half, ratio, units, line, thing, quantitative relation, number, comparison, different things, ribbon, equally divided.

expression #3 is not equivalent. the others are.