What is External Division in Geometry?

In geometry, external division is a way to divide a line segment into two parts. The parts are unequal, and the division is done by constructing a perpendicular line from one endpoint of the line segment. External division can be used to find the midpoint of a line segment, as well as any other ratio of division.

How to Perform External Division

External division can be performed using only a straightedge and compass. First, draw the line segment that is to be divided. Then, choose one endpoint of the line segment and construct a perpendicular line from that endpoint. Finally, use the compass to divide the perpendicular line into two parts in the desired ratio. The point where the two parts of the perpendicular line meet is the point of division for the original line segment. 

Uses for External Division

One common use for external division is to find the midpoint of a line segment. To do this, simply divide the line segment in half by constructing a perpendicular line and dividing it into two equal parts. The point where the two parts of the perpendicular meet will be exactly halfway between the endpoint of the original line segment.

Another common use for external division is to find any other desired ratio of division for a line segment. For example, if you want to divide a line segment into thirds, construct a perpendicular line and divide it into three equal parts. The point where the three parts of the perpendicular meet will be one-third of the way along the original line segment from its endpoint. 

Conclusion: 

External division is a powerful tool that can be used for many different purposes in geometry. Whether you're looking to find the midpoint of a line segment or divide it into any other desired ratio, external division can help you get there. All you need is a straightedge and compass!

FAQ

What is internal and external division?

In geometry, internal division is a way to divide a line segment into two parts. The parts are unequal, and the division is done by constructing a perpendicular line from one endpoint of the line segment. External division can be used to find the midpoint of a line segment, as well as any other ratio of division.

How do you find the midpoint of a line segment using external division?

To find the midpoint of a line segment using external division, simply divide the line segment in half by constructing a perpendicular line and dividing it into two equal parts. The point where the two parts of the perpendicular meet will be exactly halfway between the endpoint of the original line segment.

How do you derive the external division formula?

The external division formula can be derived by constructing a perpendicular line from one endpoint of the line segment and bisecting it. The point where the two parts of the perpendicular meet will be exactly halfway between the endpoint of the original line segment.

How do you divide a line segment externally in a given ratio?

To divide a line segment externally in a given ratio, simply construct a perpendicular line from one endpoint of the line segment and divide it into two parts in the desired ratio. The point where the two parts of the perpendicular meet will be in the desired ratio from the endpoint of the original line segment.

What is an application of external division?

External division can be used to find the midpoint of a line segment, as well as any other ratio of division. It is also useful in geometry for constructing perpendicular lines and bisecting angles.

How do you know if a point divides a line internally or externally?

If a point divides a line internally, then the two parts of the line will be unequal. If a point divides a line externally, then the two parts of the line will be equal. To determine which is which, simply construct a perpendicular line from one endpoint of the line segment and divide it into two parts. If the two parts are equal, then the point divides the line externally. If the two parts are unequal, then the point divides the line internally.