In this article, we will look at sections of a line segment. Further, we will learn the section formula, which will help us solve problems relating to position vector formula effectively. Let's find out …

In the fig given below OB is the perpendicular bisector of the line segment DE,F A⊥OB and F E intersects OB at the point C. Prove that 1 OA 1 OB = 2 OC.

In the figure, if the line segment DF intersects the side AC of a triangle ABC at the point E such that E is the midpoint of CA and AEF = AF E, prove that BD CD = BF CE.

Point P divides the line segment joining the points A(−1,3) and B(9,8) such that AP P B = k 1. If P lies on the line x−y+2 =0, find the value of k.

Find the ratio in which the line 2x+3y−5= 0 divides the line segment joining the points (8, 9) and (2, 1). Also, find the coordinates of the point of division.

In what ratio does the line x−y−2 = 0 divide the line segment joining the points(3,−1) and (8,9)? Also, find co-ordinates of point of intersection.

Find the ratio in which the y-axis divides the line segment joining points (5, − 6) and (− 1, − 4). Also, find the point of intersection.

Find the co-ordinates of the points which divide the line segment joining A(−7,5) and B(5,−1) into three congruent segments (Such points are called the points of trisection of segment).

Point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.

Line-segment AB is parallel to another line-segment CD.O is the mid-point of AD. Show that O is also the midpoint of BC.