Question

7. Find the coordinates of the points of trisection of the line segment joining (4-1)
and (-2,-3).

​

Answer 1

Step-by-step explanation:

Given coordinates are(x

1

,y

1

)=(4,−1)

and (x

2

,y

2

)=(−2,−3)

Means of trisection:- A line segment in three equal parts then ratio is 1:2 and 2:1 internally.

Case (1) If m

1

:m

2

=1:2

Then, using formula

(x,y)=(

m

1

+m

2

m

1

x

2

+m

2

x

1

,

m

1

+m

2

m

1

y

2

+m

2

y

1

)

(x,y)=(

1+2

1×(−2)+2×4

,

1+2

1×(−3)+2×(−1)

)

(x,y)=(

3

−2+8

,

3

−3−2

)

(x,y)=(2,−

3

5

)

Case (2):-

If m

1

:m

2

=2:1

Then, using formula

(x,y)=(

m

1

+m

2

m

1

x

2

+m

2

x

1

,

m

1

+m

2

m

1

y

2

+m

2

y

1

)

(x,y)=(

2+1

2×(−2)+1×4

,

1+2

2×(−3)+1×(−1)

)

(x,y)=(

3

−4+4

,

3

−6−1

)

(x,y)=(0,−

3

7

)

Hence, this is the answer.