division of line segment
DESCRIPTION
anal geomTRANSCRIPT
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By: Winnie W. PoliTeacher – III, Math dept.
MNHS
DIVISION OF LINE SEGMENT
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Internal DivisionThe point of division is on the line segment
External DivisionThe point of division lies
on the extension
Division of line Segment
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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
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12
1
21
1
yy
yy
PP
PP
12
1
yy
yyr
)( 121 yyryy
Division of Line segment Formula
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Division of Line segment Formula
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The points P1 (-4,3) & P2(2,7) determine a
line segment. Find:
a.The coordinates of the midpoint of the segment.
Problem 1
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b.) The coordinates of the trisection point nearer P2.
Problem 1
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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
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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.
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Problem 3Find the coordinates of the point which is two – thirds of the way from (3, 2) to (-3, 5).
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Problem 4Find the coordinates of the point which is two – fifths of the way from (3, 2) to (-3, 5).
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Problem 5Find the coordinates of the centroid of the triangle whose vertices are A(2, -4), B(8, 4) and C (0, 6)
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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.
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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.
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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.