Division of a Line Segment‌

A line is a never-ending ray of points. It can extend in both directions up to infinity. It is represented by arrows on both sides of the line. A line segment is a line between two stagnant points. It is restricted to two points and does not grow up to infinity. It is represented by two dots denoting the end of the line. Division of line segments helps construct triangles, measure values while working in an industry where one cannot use a ruler and a scale.

Division of a line segment

A line segment can be divided into any number of parts. These parts can be equal or unequal or can be in some ratio. We can divide a line segment into parts in two ways-

Properties of Right Circular Cylinder

  • Dividing the line segment by knowing the values – In this method, we take a ruler and pencil and simply divide the line segment by measuring the values on the ruler. Perform the steps to divide a line segment by ruler and pencil-

a. Draw a line of any length.

b. Mark a first point X on the line. This will be your starting point.

c. For instance, you want to divide the line into 5cm and 4cm values. Keep the ruler at point X, and draw the line up to 5cm from the ruler on the line—Mark the endpoint as Y.

d. Now take 4cm on the ruler, place the ruler at point Y, and draw the line up to 4cm. Mark this point as Z.

e. Therefore, lines XY = 5cm and YZ = 4cm, which you wanted.

This method is used when we need to draw the line segment by knowing values. Make sure the initial line drawn for reference must be straight.

  • Dividing the line segment in ratios – This method is used when we do not know the values of the line segment that we need to divide. Instead, we know the ratios that we want to construct. Perform the steps to divide the line based on ratios-

a. Draw a reference line of any length.

b. Suppose we need to draw a line segment in the ratio 5:1. Take any numbers that have the ratio of 5:1. Try to choose small numbers that fit the line you have drawn for reference.

c. We can also take 5cm and 1cm to represent the ratios.

d. Take 5cm on the compass measured from the scale. Keep the compass measurements clear and accurate.

e. Choose a point P on the line segment, place the compass on that point, and draw an arc on the line segment. The point where the arc meets the line segment is Q and is 5cm in length.

f. If the line were not 5cm, there would have been an error while choosing the dimensions on the compass.

g. Similar way, choose 1cm on the compass. With Q as the starting point, mark an arc on the line segment. Name it R. h. Therefore, the required line segments PQ = 5cm and QR = 1cm, and are in the ratios 5:1.