Introduction For Geometry Line Segment
The term ‘Geometry’ means a study properties of figures and shape diagrams and relationship between them. Geometry is the important branches of a Mathematics. In a real life geometry plays an important role from the concept of geometry have begun from ancient times. Geometry gives idea for the various geometrical shapes and figures. A line segment which is a connected piece of line. line segment has two endpoints and is named by its endpoints. Sometimes, the symbol – written on top of two letters is used to denote the segment.
Geometry Line Segment Problems:
Ex 1:
Find the point which divides line segment which joins the point (–1, 2) and (4,–5) internally in the ratio 2:3.
Sol:
The required point is given by
` ((mx2+nx1)/(m+n),(my2+ny1)/(m+n))`
(x1,y1)=(-1,2) (x2,y2)=(4,-5)
m:n=2:3
=`((2xx4+3xx(-1))/(2+3),(2xx(-5)+3xx2)/(2+3))`
=`((8-3)/5,(-10+6)/5)`
=`5/5,-4/5`
=(1,-4/5)
Ex 2:
Find the point which divides the line segment joining the points (2,1) and (3,5) externally in the ratio 2:3.
Sol:
The required point is given by
` ((mx1-nx2)/(n-m),(my1-ny2)/(n-m))`
(x1,y1)=(2,1),(x2,y2)=(3,5) m:n=2:3
=`((3xx2 -2xx3)/(3-2),(3xx1-2xx5)/(3-2))`
=`(6-6)/1,(3-10)/1`
=(0,-7)
Ex 3:
Find the co-ordinates of the mid point of the line segment joining the points A(–3,2) and B(7,8)
Sol:
The required mid point is
(x1,y1)=(-3,2),(x2,y2)=(7,8)
Formula` ((x1+x2)/2,(y1+y2)/2)`
`((-3)+7)/2, (2+8)/2`
` (4/2,10/2)` =(2,5)
Ex 4:
Find the co-ordinates of the mid point of the line segment joining the points A(2,3) and B(4,5)
Sol:
The required mid point is (x1,y1)=(2,3),(x2,y2)=(4,5)
Formula `((x1+x2)/2,(y1+y2)/2)`
=`((2+4)/2, (3+5)/2)`
=`(6/2,18/2) `
=(3,9)
Between, if you have problem on these topics solve my math problems for me, please browse expert math related websites for more help on math word problems for 5th grade.
Geometry Line Segment : Slope of Line Segment Problems:
Ex 1:
Find the slope of the line passing through (5,6) and (15,9)
Sol:
Take (5,6) as (x1, y1) and (15, 9) as (x2, y2).
m=`(y2-y1)/(x2-x1)`
=`(9-6)/(15-5)`
=`3/10`
Ex 2:
Find slope of line which passing through (-16, 29) and (40, -6)
Sol:
The slope of the line is
m=`(y2-y1)/(x2-x1)`
m =`(-6-29)/(40-(-16)) `
= `-35/56`
=`-5/8`
The term ‘Geometry’ means a study properties of figures and shape diagrams and relationship between them. Geometry is the important branches of a Mathematics. In a real life geometry plays an important role from the concept of geometry have begun from ancient times. Geometry gives idea for the various geometrical shapes and figures. A line segment which is a connected piece of line. line segment has two endpoints and is named by its endpoints. Sometimes, the symbol – written on top of two letters is used to denote the segment.
Geometry Line Segment Problems:
Ex 1:
Find the point which divides line segment which joins the point (–1, 2) and (4,–5) internally in the ratio 2:3.
Sol:
The required point is given by
` ((mx2+nx1)/(m+n),(my2+ny1)/(m+n))`
(x1,y1)=(-1,2) (x2,y2)=(4,-5)
m:n=2:3
=`((2xx4+3xx(-1))/(2+3),(2xx(-5)+3xx2)/(2+3))`
=`((8-3)/5,(-10+6)/5)`
=`5/5,-4/5`
=(1,-4/5)
Ex 2:
Find the point which divides the line segment joining the points (2,1) and (3,5) externally in the ratio 2:3.
Sol:
The required point is given by
` ((mx1-nx2)/(n-m),(my1-ny2)/(n-m))`
(x1,y1)=(2,1),(x2,y2)=(3,5) m:n=2:3
=`((3xx2 -2xx3)/(3-2),(3xx1-2xx5)/(3-2))`
=`(6-6)/1,(3-10)/1`
=(0,-7)
Ex 3:
Find the co-ordinates of the mid point of the line segment joining the points A(–3,2) and B(7,8)
Sol:
The required mid point is
(x1,y1)=(-3,2),(x2,y2)=(7,8)
Formula` ((x1+x2)/2,(y1+y2)/2)`
`((-3)+7)/2, (2+8)/2`
` (4/2,10/2)` =(2,5)
Ex 4:
Find the co-ordinates of the mid point of the line segment joining the points A(2,3) and B(4,5)
Sol:
The required mid point is (x1,y1)=(2,3),(x2,y2)=(4,5)
Formula `((x1+x2)/2,(y1+y2)/2)`
=`((2+4)/2, (3+5)/2)`
=`(6/2,18/2) `
=(3,9)
Between, if you have problem on these topics solve my math problems for me, please browse expert math related websites for more help on math word problems for 5th grade.
Geometry Line Segment : Slope of Line Segment Problems:
Ex 1:
Find the slope of the line passing through (5,6) and (15,9)
Sol:
Take (5,6) as (x1, y1) and (15, 9) as (x2, y2).
m=`(y2-y1)/(x2-x1)`
=`(9-6)/(15-5)`
=`3/10`
Ex 2:
Find slope of line which passing through (-16, 29) and (40, -6)
Sol:
The slope of the line is
m=`(y2-y1)/(x2-x1)`
m =`(-6-29)/(40-(-16)) `
= `-35/56`
=`-5/8`
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