Question

find the coordinates of the points of trisection of the line segment joining the points A (2,-2) and B (-7,4)

Answer 1

let p and q be the point of trisection
let p divides in ratio 1:2
then m1/m2 =1/2
a(x1,y1)=(2,-3) and b(x2,y2)=(4,-1)
p(x,y)=p(m1x2+m2x1/m1+m2,m1y2+m1y2/m1+m2)
=p(1×-7+2×2/1+2,1×4+2×-2/1+2)
=p(-7+4/3,4-2/3)
=p(-1,2/3)
let q divides ab in ratio 2:1
then, m1/m2=2/1
a(x1,y1)=(2,-3) and b (x2,y2)=(4,-1)
=q(2×-7+1×2/2+1/2×4+1×-2/2+1)
=q(-17/3,2)
hence the value of p and q are acquired.

Answer 2

Answer:

let p and q be the point of trisection

let p divides in ratio 1:2

then m1/m2 =1/2

a(x1,y1)=(2,-3) and b(x2,y2)=(4,-1)

p(x,y)=p(m1x2+m2x1/m1+m2,m1y2+m1y2/m1+m2)

=p(1×-7+2×2/1+2,1×4+2×-2/1+2)

=p(-7+4/3,4-2/3)

=p(-1,2/3)

let q divides ab in ratio 2:1

then, m1/m2=2/1

a(x1,y1)=(2,-3) and b (x2,y2)=(4,-1)

=q(2×-7+1×2/2+1/2×4+1×-2/2+1)

=q(-17/3,2)

hence the value of p and q are acquired.

Step-by-step explanation: