Question

Find the points of trisection of line segment joining (-4,5) and (3,-7).

Answer 1

Answer:

Trisection means dividing a line segment in three equal parts or dividing a line segment in the ratio 1:2 and 2:1

Given points: x

1

=3,x

2

=−3,y

1

=−2,y

2

=−4

CASE :- 1

m:n=1:2

=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

=(

2+1

1(−3)+(3)

,

2+1

1(−4)+2(−2)

)

=(

3

−3+6

,

3

−4−4

)

=(−1,

3

−8

)

CASE :- 2

m:n=2:1

=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

=(

2+1

2(−3)+1(3)

,

2+1

2(−4)+1(−2)

)

=(

3

−6+3

,

3

−8−2

)

=(

3

−3

,

3

−10

)

=(−1,

3

−10

)

Answer 2

Given coordinates are (x1,y1) = (4, - 1) and (x2,y2) = ( - 2, - 3 ) Means of trisection: - A line segment in three equal parts then ratio is 1:2