Solution: The Steps are defined below,
Explanation:
To divide a line segment in 2:3 using compass alexis has to follow many steps:
1) Draw a line segment ab of length x.
2) Draw a line ac which makes an acute angle with the line ab.
3) Since alexis has to divide the line is 2:3, so make 2+3=5 arc of equal length of ac with the help of compass.
4) Name the fifth arc as d, so join the fifth arc with point b.
5) The draw a parallel to the line bd, and passing through the 2nd acr of ad. mark the second are as m.
6) Let the parallel line intersect at point n. Where the parallel line intersect the line ab, that point divides the line segment ab is 2:3.
By using above steps we get the figure same as the figure given below.
The line [tex]\bf ab[/tex] can be divided into the ratio [tex]2:3[/tex] with the help of a compass.
Further explanation:
Given that Alexis is trying to partition a line segment [tex]\bf ab[/tex] in the ratio [tex]2:3[/tex] with the help of compass.
There are different methods to divide a line segment in the given ratio, but we will use a simple method to divide the line [tex]\bf ab[/tex] in the ratio [tex]2:3[/tex].
Given a line segment [tex]\bf ab[/tex], which is to be divided in the ratio of [tex]2:3[/tex].
First draw any ray [tex]\bf ax[/tex] which makes an acute angle with [tex]\bf ab[/tex].
Locate [tex]5[/tex] points [tex]\bf a_{1},a_{2},a_{3},a_{4}\text{ and }a_{5}[/tex] on the ray [tex]\bf ax[/tex] such that [tex]\bf aa_{1},a_{1}a_{2},a_{2}a_{3},a_{3}a_{4}[/tex] and [tex]\bf a_{4}a_{5}[/tex] are equal, with the help of a compass.
Since, Alexis is trying to divide the line [tex]\bf ab[/tex] into the ratio of [tex]2:3[/tex], therefore, the ray [tex]\bf ax[/tex] is divided into [tex]5(2+3)[/tex] points.
Now, join the point [tex]\bf b[/tex] with the point [tex]\bf a_{5}[/tex].
From the point [tex]\bf a_{2}[/tex], draw a line parallel to [tex]\bf ba_{5}[/tex] and this can be drawn by making an angle equal to [tex]\angle\text{aa}_{5}\text{b}[/tex].
Now, consider that the line that is drawn parallel to [tex]\bf ba_{5}[/tex] intersect the given line [tex]\bf ab[/tex] at the point [tex]\bf c[/tex].
The point of intersection on the line [tex]\bf ab[/tex] is the point where it is divided into the ratio [tex]2:3[/tex] as shown in Figure 1 (attached in the end).
The above used steps are used to divide any line in the given ratio.
Therefore, the line [tex]\bf ab[/tex] can be divided into the ratio of [tex]2:3[/tex].
Learn more:
1. Learn more about angles https://brainly.com/question/1953744
2. Learn about collinear points https://brainly.com/question/5191807
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Constructions
Keywords: Alexis, compass, partition, segment, ab, ratio, 2:3, constructions, line, ray, parallel, intersection, angle, acute, geometry, line segment, acute angle.
