Question

find the corrrdinates of the point of trisection on line segment joining (4.-1)and(-2-3)
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Answer 1

Answer:

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 and 2:1 internally.

Case (1) If m1:m2=1:2

Then, using formula

(x,y)=(m1+m2m1x2+m2x1, m1+m2m1y2+m2y1)

(x,y)=(1+21×(−2)+2×4,1+21×(−3)+2×(−1) )

(x,y)=(3−2+8, 3−3−2)

(x,y)=(2,− 35)

Case (2):-If m1:m2=2:1

Then, using formula

(x,y)=(m1+m2m1x2+m2x1,m1+m2m1y2+m2y1)

(x,y)=(2+12×(−2)+1×4, 1+22×(−3)+1×(−1))

(x,y)=(3−4+4, 3−6−1)

(x,y)=(0,− 37)