Geometry give g(1,2) and k(8,12). find the coordinates of p that partitions gk in the ratio of 3: 2

A point P on the line segment GK may be parametrically represented as

t is a real parameter which controls where on the segment P is.  t=0 means P=G, t=1 means P=K.  We're interested in the t that gives a 3:2 ratio for PG:PK.  That's closer to K so t>1/2.   t=3/(3+2) = 3/5.

(26/5, 8)

(5.2, 8)

Step-by-step explanation:

Given : G(1,2) and K (8,12).

To find :  The coordinates of P that partitions gk in the ratio of 3:2

Section formula :

The line segment having endpoints (a,b) and (c,d) is divided in ration m:n by point M , then the coordinates of the M will be :-

Similarly,

Now simplify , we get

x=5.2  and y=8

Hence, the coordinates of P that partitions GK in the ratio of 3:2 = (5.2, 8)

a) t'(-3, 6) and v'(0, 3)  

step-by-step explanation: