State the theorem of triangle which is used for dividing a line segment in a given ratio.
The theorem you are referring to is known as the "Section Formula" or "Internal Division Theorem." It states that if a line segment AB is divided by a point P, such that it is divided in the ratio of m:n internally, then the coordinates of point P can be found using the following formula:
The x-coordinate of point P = [(n * x-coordinate of point A) + (m * x-coordinate of point B)] / (m + n)
The y-coordinate of point P = [(n * y-coordinate of point A) + (m * y-coordinate of point B)] / (m + n)
To apply this theorem, you need to know the coordinates of points A and B, as well as the ratio m:n in which the line segment AB is divided. By substituting these values into the formula, you can calculate the coordinates of point P, which represents the division point of the line segment AB.