# Division of a line segment in the given ration internally

Before I state my problem description, would like to describe problem which was stated before my problem. So it is like this

Given a line segment $AB$. You are required to divide it internally in the ratio $2 : 3$. steps for this problem is following

1. Draw a ray $AC$ making an acute angle with $AB$.

2. Starting with $A$, mark off 5 points $C_1, C_2, C_3, C_4, C_5$ at equal distances from the point $A$.

3. Join $C_5$ and $B$
4. Through $C_2$ (i.e. the second point), draw $C_2D$ parallel to $C_5B$ meeting $AB$ in $D$.

Then $D$ is required point, which divides $AB$ segment into $2:3$ part.

Here is picture which demonstrate this procedure: based on this information, I am trying to solve similar one

Draw a line segment 7 cm long. Divide it internally in the ratio $3 : 4$. Measure each part. Also write the steps of construction.

So as I understood, because we had to divide into ratio $2:3$ and we took $5$ points,in our case we have to take $7$ points right? Because of $3:4$ ration, with equal distance from starting $A$, of course first we should draw ray with acute angle,then took $7$ point,connect last point to one of the end of our segment (which equal to $7$cm) then choose $C_3$ and connect segment, intersection point would be desired point yes? Please tell me if I am wrong, also what should be length of each small segments, by which we divide large one?

• yes it is right Apr 25, 2012 at 11:29
• By small segments you mean those with the seven point (and A) as endpoints? It does not matter what their length is, anything constructable. Just make them the same. Apr 25, 2012 at 12:16
• so my argument is correct? Apr 25, 2012 at 13:25
• @dato: Yes, your method is correct for the ratio $3:4$, and generalizes in a straightforward way to the ratio $m:n$, where $m$ and $n$ are positive integers. It all comes down to properties of parallel lines (you get equal angles, so similar triangles), or to put it another way, properties of scaling. Apr 25, 2012 at 14:36
• thanks very much @André Nicolas Apr 26, 2012 at 6:27