Answer:
We found the coordinates of point [tex]P[/tex] [tex](x,y)[/tex] ≡ [tex](1,1)[/tex].
Step-by-step explanation:
Labelled Diagram has shown below.
Given that,
Coordinates of a line segment [tex](-5,5) \ to \ (10,-5)[/tex] of the directed line.
The line segment is section into ratio of 2:3.
From the Question,
Let the coordinates of given points as[tex]M[/tex] [tex](-5,5)[/tex] & [tex]N[/tex] [tex](10,-5)[/tex].
Sectioned ratio of the line segment is [tex]2:3[/tex] by point P [tex](x,y)[/tex].
Now,
Using Section Formula,
[tex]x=\frac{mx_{2} + nx_{1} }{m+n} }[/tex] , [tex]y=\frac{my_{2}+ny_{1} }{m+n}[/tex]
Then Substituting all the coordinates we get the [tex]P[/tex] [tex](x,y)[/tex]
[tex]x=\frac{2\times 10+3\times -5}{2+3} =\ \frac{20-15}{5}= \ 1[/tex]
[tex]y=\frac{2\times -5 + 3\times 5}{2+3}=\ \frac{-10+15}{5} = 1[/tex]
Therefore, We found the coordinates of point [tex]P[/tex] [tex](x,y)[/tex] ≡ [tex](1,1)[/tex].
