Question

Geometry

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

Answer 1

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

`P = (1-t)G + tK`

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.

`P=(1-3/5)(1,2) + (3/5)(8,12) = (2/5,4/5)+(24/5,36/5)=(26/5,40/5)=(26/5,8)`

Answer: (26/5, 8)

Answer 2

Answer: (5.2, 8)

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 :-

`x=(mc+na)/(m+n)\ ;\ y=(md+nb)/(m+n)`

Similarly,

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

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)