Question

given G (1,2) and K(8,12) what does it mean to find the point P on line GK such that 3 (GP) = 2 (PK)?

Answer 1

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Answer 2

The coordinates of point P is (3.8,6)

Explanation:

We are given that 3 (GP) = 2 (PK)

So,
`(GP)/(PK)=(2)/(3)` ---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 :
`x=(mx_2+nx_1)/(m+n) , y=(my_2+ny_1)/(m+n)`

m:n = 2:3

`G =(x_1,y_1)=(1,2)`

`K =(x_2,y_2)=(8,12)`

Substitute the values in the formula

`x=(mx_2+nx_1)/(m+n) , y=(my_2+ny_1)/(m+n)`

`x=(2(8)+3(1))/(2+3), y=(2(12)+3(2))/(2+3)`

`x=3.8  , y=6`

Hence the coordinates of point P is (3.8,6) .