Question

Find the co-ordinates of the points of trisection of the line segment joining the point A(1,-2)and B(-3,4)​

Answer 1

Answer:

trisection means 2:1=m:n

coordinates = (mx2+nx1)/m+n;(my2+ny1)/m+n

= (2(-3)+1(1)/2+1;2(4)+1(-2)/2+1)

=(-5/3;2)

Answer 2

Step-by-step explanation:

.A(1,-2)___________C(x,y)._____________B(-3,4)

the points which divides the line AB in the ratio 2:1 and 1:2 are called points of trisection of the line AB.

let the point of trisection be P(x,y).And the ratio is 2:1

then, P(x,y)=[mx2+nx1/m+n,my2+ny1/m+n]

P(x,y)=[2(-3)+1(1)/2+1,2(4)+1(-2)/2+1]

P(x,y)=[-6+1/3,8-2/3]

P(x,y)=[-5/3,6/3]

P(x,y)=[-5/3,2]

let another point of trisection be Q(x',y'). And the ratio is 1:2

Q(x',y')=[mx2+nx1/m+n,my2+ny1/m+n]

Q(x',y')=[1(-3)+2(1)/1+2,1(4)+2(-2)/1+2]

Q(x',y')=[-3+2/3,4-4/3]

Q(x',y')=[-1/3,0]

hope this helps you