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.

Answer 2

The half -length of the directed line segment is $\boxed{{\mathbf{not same}}}$  as the length of the directed line segment is divided into the ratio of $1:2$ .

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 $1:2$ .

Step by step explanation:

Step 1

The directed line segment is divided in the ratio of $1:2$ .

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 $1:2$ .

$\begin{aligned}{\text{first part}}&=\frac{1}{3}\times6=2\hfill\\{\text{second part}}&=\frac{2}{3}\times6=4\hfill\\\end{aligned}$

Therefore, the ribbon is partitioned in the ratio of $1:2$  as ${\text{2cm, 4cm}}$  

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

  $\frac{1}{2}\times 6=3$

Therefore, the ribbon is partitioned into half as ${\text{3cm, 3cm}}$ .

Thus, it has been proved the given explanation.

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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.