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Lesson 4 division of a line segment
The document discusses dividing a line segment into parts at given ratios. It defines the point of division as the point that divides a line segment into a given ratio. It then presents the formula to find the point of division using similar triangles. The document provides examples of finding the point of division for line segments divided into equal parts or divided at specific ratios. It gives examples of finding the midpoint and trisection points of line segments.
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Introduction to the concept of dividing a line segment by Prof. Teresita P. Liwanag – Zapanta.
Definition of point of division, which divides a line segment in a given ratio.
Equation derived from similar triangles for solving for specific points on a line segment.
Various examples detailing how to find division points, midpoints, and coordinate calculations with given points.
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Lesson 4 division of a line segment
- 1. DIVISION OF ALINE SEGMENT Prepared by: Prof. Teresita P. Liwanag – Zapanta B.S.C.E., M.S.C.M., M.Ed. (Math-units), PhD-TM (on-going)
- 2. DIVISION OF ALINE SEGMENT POINT OF DIVISION – is a point that divides a line segment to a given ratio.
- 3. By Similar Triangles: x – x1 = rx2 – rx rx + x = x1 + rx2 x( 1 + r ) = x1 + rx2 Solving for x solving for y
- 4. Examples: 2.The line segment joining (-5, -3) and (3, 4) is to be divided into five equal parts. Find the point of division closest to (-5, -3). 3.Find the midpoint of the segment joining (7, -2) and (-3, 5). 4.The line segment from (1, 4) to (2, 1) is extended a distance equal to twice its length. Find terminal point. 5.On the line joining (4, -5) to (-4, -2), find the point which is three-seventh the distance from the first to the second point. 6.Find the trisection points of the line joining (-6, 2) and (3, 8). 7.The midpoints of the sides of a triangle are A(3, 0), B(5, 2), C(2, 2). 8.Three consecutive vertices of a parallelogram are A(6, 1), B(-2, 3), C(-6, 0). Find the coordinates of the fourth vertex.