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Problem: trisection points (-2,3) and (5,4) [ Calculator, Method and examples ]

Solution:
Your problem `->` trisection points (-2,3) and (5,4)


Suppose P(x,y) divides AB in the ratio 1:2.
Here `A(-2,3), B(5,4)` are the given points

`:. x_1=-2, y_1=3, x_2=5, y_2=4`


`:. x=(mx_2+nx_1)/(m+n)`

`=(1*5+2*-2)/(1+2)`

`=(5-4)/(3)`

`=(1)/(3)`

`=0.3333`

`:. y=(my_2+ny_1)/(m+n)`

`=(1*4+2*3)/(1+2)`

`=(4+6)/(3)`

`=(10)/(3)`

`=3.3333`

`:.` P is (0.33,3.33)

Suppose Q(x,y) divides AB in the ratio 2:1.
Here `A(-2,3), B(5,4)` are the given points

`:. x_1=-2, y_1=3, x_2=5, y_2=4`


`:. x=(mx_2+nx_1)/(m+n)`

`=(2*5+1*-2)/(2+1)`

`=(10-2)/(3)`

`=(8)/(3)`

`=2.6667`

`:. y=(my_2+ny_1)/(m+n)`

`=(2*4+1*3)/(2+1)`

`=(8+3)/(3)`

`=(11)/(3)`

`=3.6667`

`:.` Q is (2.67,3.67)

TriSection Points are (0.33,3.33) and (2.67,3.67)









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