Answer:
The coordinate of point P(x,y) is, [tex](\frac{11}{4} ,1)[/tex]
Step-by-step explanation:
Let the coordinate of the point P be (x,y) .
A point P divides a segment GH internally in the ratio m:n, to find the coordinate of point P we use the section formula :
The coordinate of point
[tex]P(x,y) = (\frac{mx_{2}+nx_{1}}{m+n} , \frac{my_{2}+ny_{1}}{m+n})[/tex]
Then, to find the co-ordinates of the point P dividing the line segment GH joining two given points in a given ratio i.e m:n= 1:3.
Then,
[tex]x= \frac{mx_{2}+nx_{1}}{m+n}[/tex]
[tex]x=\frac{1\cdot 8+3\cdot 1}{1+3} =\frac{8+3}{4}=\frac{11}{4}[/tex].
For y:
[tex]y= \frac{my_{2}+ny_{1}}{m+n}[/tex]
[tex]y=\frac{1\cdot 1+3\cdot 1}{1+3} =\frac{1+3}{4}=\frac{4}{4}=1[/tex].
Therefore, the coordinate of point P(x,y) is, [tex](\frac{11}{4} ,1)[/tex]
