Question

find the coordinates of the points trisection of the line segment joining 4 -1 and -2 -3 ​

Answer 1

Step-by-step explanation:

Suppose Points P and Q trisect the line segment joining the pointsA(4,1) and B(2,3)

This means, P divides AB in the ratio 1:2 and Q divides it in the ratio 2:1

Using the section formula, if a point (x,y) divides the line joining the

points (x

1

,y

1

) and (x

2

,y

2

) internally

in the ratio m:n, then (x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Substituting (x

1

,y

1

)=(4,−1) and (x

2

,y

2

)=(−2,−3) and m=1,n=2 in the section formula, we get

the point P =(

1+2

1(−2)+2(4)

,

1+2

1(−3)+2(−1)

)=(2,−

3

5

)

Substituting (x

1

,y

1

)=(4,−1) and (x

2

,y

2

)=(−2,−3) and m=2,n=1 in the section formula, we

get the point Q =(

2+1

2(−2)+1(4)

,

2+1

2(−3)+1(−1)

)=(0,−

3

7

)