Question

the coordinates of points of trisection of line segment joining (-2,4) and (3,-2) are​

Answer 1

Answer:

The coordinates of points of trisection of line segment PQ are A ≡ ($\frac{-1}{3} , 2$) and B ≡ ($\frac{4}{3} , 0$).

Step-by-step explanation:

Let given points be P(-2,4) and Q(3,-2). Also, let points of trisection of line segment PQ be A(divides PQ in ratio 1:2) and B(divides PQ in ratio 2:1).

w.k.t, the co-ordinates of point which divide a line segment joining two points (x₁,y₁) and (x₂,y₂) in the ratio m:n are ≡ ($\frac{mx_{2}+nx_{1}}{m+n} , \frac{my_{2}+ny_{1}}{m+n}$).

⇒ Co-ordinates of point A = ($\frac{1.3+2.(-2)}{1+2} , \frac{1.(-2)+2.4}{1+2}$) = ($\frac{3-4}{3} , \frac{-2+8}{3}$)

or A ≡ ($\frac{-1}{3} , 2$)

And, co-ordinates of point B = ($\frac{2.3+1.(-2)}{2+1} , \frac{2.(-2)+1.4}{2+1}$) = ($\frac{6-2}{3} , \frac{-4+4}{3}$)

or B ≡ ($\frac{4}{3} , 0$)

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