Question

Given G (1,2) and K(8,12) Part A what does it mean to find the point ponline gk such that 3(GP)=2(PK)?

Answer 1

Refer to the diagram shown below.

Let the coordinates of P be (x,y).

Because 3(GP) = 2(PK), therefore
3(x-1) = 2(8-x)
3x - 3 = 16 - 2x
5x = 19
x = 3.8

Similarly,
3(y-2) = 2(12-y)
3y - 6 = 24 - 2y
5y = 30
y = 6

Answer:
The coordinates of P are (3.8, 6)