By: Winnie W. PoliTeacher – III, Math dept.

MNHS

DIVISION OF LINE SEGMENT

Internal DivisionThe point of division is on the line segment

External DivisionThe point of division lies

on the extension

Division of line Segment

From similar triangles, we can find the x – coordinate of P as follows:

12

1

21

1

xx

xx

PP

PP

12

1

xx

xxr

)( 121 xxrxx

Division of Line segment Formula

12

1

21

1

yy

yy

PP

PP

12

1

yy

yyr

)( 121 yyryy

Division of Line segment Formula

Division of Line segment Formula

The points P1 (-4,3) & P2(2,7) determine a

line segment. Find:

a.The coordinates of the midpoint of the segment.

Problem 1

b.) The coordinates of the trisection point nearer P2.

Problem 1

A point P is on the line passing through A (-2, 5) and B (4, 1). Finda. The coordinates of P if it is twice as far from A as from B

Problem 2

A point P is on the line passing through A (-2, 5) and B (4, 1). Find the coordinates of P if it is thrice times as far from B as from A.

Problem 3Find the coordinates of the point which is two – thirds of the way from (3, 2) to (-3, 5).

Problem 4Find the coordinates of the point which is two – fifths of the way from (3, 2) to (-3, 5).

Problem 5Find the coordinates of the centroid of the triangle whose vertices are A(2, -4), B(8, 4) and C (0, 6)

Problem 6Find the coordinates of the point which divides the line segment connecting (-1, 4) and (2, -3) into two parts which have the ratio 3/2.

Problem 7The line segment joining A(1, 3) and B(-2, -1) is extended through each end by a distance equal to its original length. Find the coordinates of the new endpoints.

Problem 8Find the coordinates of P if it divides the line segment through a(1, -5) and B(7, -2) so that AP : PB = 3: 5

Problem 9The segment joining (-4, 7) and (5, -2) is divided into two segments, one of which is five times as long as the other. Find the point of division.

Problem 10The segment joining (2, -4) and (9, 3) is divided into two segments, one of which is three –fourths as long as the other. Find the point of division.

Problem 11Three consecutive vertices of a parallelogram are (5, 1), (1, 3), (-5, -1). Find the coordinates of the fourth vertex.