 Hello and welcome to the session. In this session we will learn division of a line segment in a given ratio. Suppose we are given a line segment AB and we have to divide this in the ratio m is to n where m and n are both positive integers. Let's take the line segment AB of any length and we have to divide this in the ratio 3 is to 2. So our first step would be draw a line segment AB of the given length. So this is the line segment AB. In the next step we draw a ray making an acute angle with AB. This is the ray AX and this angle is an acute angle. Next we draw a ray addled to the ray AX in which we get angle ABY to be equal to angle BAX. This is the ray BY and this angle is equal to this angle. In the next step we locate the points A1, A2, A3 that is number of points equal to m on the ray AX and points B1, B2 that is number of points equal to n on the ray BY such that we get AA1 equal to A1, A2 equal to A2, A3 equal to BB1 equal to B1, B2. As you can see we have located the points A1, A2, A3 and B1, B2. Next we join the points A3, B2. We have joined A3, B2. We mark this point at which this line intersects AB as the point C. This gives us that AC upon CB is equal to m upon n that is 3 upon 2 or AC is 2, CB is equal to 3 is 2. Hence the given line segment AB is divided in the ratio m is to n. This completes the session. Hope you have understood the concept of division of a line segment in a given ratio.