Name: Ruler and Compass Constructions
Uploaded: 2019-07-19
Duration: 9 min 30 s

Question

Draw a line segment

A B

and take a point

C

on it such that

A C : A B = 3 : 4

. Check whether

A C : C B

is

3 : 4

or not.

Accepted Answer

A line segment $A B$ is given considering a point $C$ on it such that $A C : A B = 3 : 4$

This means that the length of the line segment $A C$ is $\frac{3}{4}$ of the line segment $A B$ .

If we divide the line segment in four equal parts and select three parts out of four, then this will be $\frac{3}{4}$ of the whole line segment.

We know that a line segment which is parallel to any side of a triangle divides the remaining sides of a triangle in the same ratio.

Steps of construction:

Draw a ray $A Y$ making an acute angle at point $A$

Cut four equal arcs on $A Y$ and name them $A A_{1}, A_{1} A_{2}, A_{2} A_{3}, A_{3} A_{4}$ and all these are equally spaced $A A_{1} = A_{1} A_{2} = A_{2} A_{3} = A_{3} A_{4}$

Now join $B$ with $A_{4}$ and draw a parallel line from $A_{3}$ to $A_{4} B$ , which intersects $A B$ at $C$ .

Therefore, $A C$ is the required line segment, because $A C : A B = 3 : 4$ .

And as we can clearly see that $A C : C B \neq 3 : 4$ .

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