Answer:
The coordinates of point P is (3.8,6)
Step-by-step explanation:
We are given that 3 (GP) = 2 (PK)
So, [tex]\frac{GP}{PK}=\frac{2}{3}[/tex] ---A
P is the point of line GK which divides line in two parts GP and Pk
By A we can say that P divides the line in ratio 2:3
To find the coordinates of point P , we will use section formula.
Formula : [tex]x=\frac{mx_2+nx_1}{m+n} , y=\frac{my_2+ny_1}{m+n}[/tex]
m:n = 2:3
[tex]G =(x_1,y_1)=(1,2)[/tex]
[tex]K =(x_2,y_2)=(8,12)[/tex]
Substitute the values in the formula
[tex]x=\frac{mx_2+nx_1}{m+n} , y=\frac{my_2+ny_1}{m+n}[/tex]
[tex]x=\frac{2(8)+3(1)}{2+3}, y=\frac{2(12)+3(2)}{2+3}[/tex]
[tex]x=3.8 , y=6[/tex]
Hence the coordinates of point P is (3.8,6) .
