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

Answer:

The coordinates of point P is (3.8,6)

Step-by-step explanation:

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

So, $\frac{GP}{PK}=\frac{2}{3}$  ---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 : $x=\frac{mx_2+nx_1}{m+n} , y=\frac{my_2+ny_1}{m+n}$

m:n = 2:3

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

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

Substitute the values in the formula

$x=\frac{mx_2+nx_1}{m+n} , y=\frac{my_2+ny_1}{m+n}$

$x=\frac{2(8)+3(1)}{2+3}, y=\frac{2(12)+3(2)}{2+3}$

$x=3.8 , y=6$

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

Answer 2

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