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2 months ago

Alexis is trying to partition segment ab in the ration 2:3 using a compass

Mathematics

2 answers:

zzz [12.3K]2 months ago

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Using a compass, the line shown in $\bf ab$ can be split according to the ratio depicted in $2:3$ .

Detailed explanation:

Alexis aims to divide the line segment $\bf ab$ into parts with the ratio $2:3$ , by employing a compass.

There exist various techniques to segment a line segment in the specified ratio, but we'll use a straightforward approach here to partition the line $\bf ab$ into the ratio $2:3$ .

Consider the line segment $\bf ab$ that needs division in the ratio $2:3$ .

Begin by drawing any ray $\bf ax$ forming an acute angle with $\bf ab$ .

Mark $5$ points $\bf a_{1},a_{2},a_{3},a_{4}\text{ and }a_{5}$ on this ray $\bf ax$ so that the distances $\bf aa_{1},a_{1}a_{2},a_{2}a_{3},a_{3}a_{4}$ and $\bf a_{4}a_{5}$ are equal, utilizing a compass.

Since Alexis plans to split the line $\bf ab$ in the ratio $2:3$ , the ray $\bf ax$ will be divided into $5(2+3)$ points accordingly.

Next, connect point $\bf b$ with point $\bf a_{5}$ .

From point $\bf a_{2}$ , draw a line parallel to $\bf ba_{5}$ by replicating an angle identical to $\angle\text{aa}_{5}\text{b}$ .

This parallel line to $\bf ba_{5}$ will intersect the original line $\bf ab$ at point $\bf c$ .

The intersection point $\bf ab$ represents the exact spot where the line is divided into the ratio $2:3$ , as illustrated in Figure 1 at the end.

The outlined procedure can be applied to split any line segment into a given ratio.

Therefore, the line $\bf ab$ has been successfully sectioned in the ratio $2:3$ .

For additional study:

1. Explore more about angles brainly.com/question/1953744

2. Understand collinear points brainly.com/question/5191807

Answer specifics:

Grade level: High school

Subject area: Mathematics

Topic: Constructions

Key terms: Alexis, compass, partition, segment, ab, ratio, 2:3, constructions, line, ray, parallel, intersection, angle, acute, geometry, line segment, acute angle.

AnnZ [12.3K]2 months ago

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Solution: The procedure is outlined below,

Steps:

To divide the line segment into a 2:3 ratio using a compass, Alexis should:

1) Sketch the line segment ab of length x.

2) Draw another line ac forming an acute angle with ab.

3) Since the ratio is 2:3, count 2+3=5 equal arcs along ac using the compass.

4) Label the fifth arc as point d, then connect d to point b.

5) Draw a line parallel to bd through the second arc along ad, marking it as m.

6) The intersection point n of this parallel line with ab divides ab in the 2:3 ratio.

Using these steps creates a figure as shown below.

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The question appears to be incomplete. Here’s the complete inquiry:

Samir is quite skilled with the gun. When he targets a specific aim at the shooting range, he has a 0.95 probability of striking it. On one occasion, Samir sets out to shoot 10 targets consecutively.

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Step-by-step breakdown:

Let 'A' represent the event of successfully hitting all targets in 10 trials.

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