Calculate force due to gravity between two points

Question

If I have point $A$ at $(0,0)$ and point $B$ at $(2,2)$, each with a mass of 100, I think I need to calculate the final force first $\frac{GMm}{r^2}$ and then work out the components of that force that go in the x and y direction.

Or can I just multiply the final force by the $ \Delta x$ or the $ \Delta y $?

Answer 1

Using your formula for gravity you will find the force between them, along the vector $(2,2)$.

If you want to calculate the components in the x- and y-direction, you can use for example Pythagoras' theorem (the length of the hypotenuse is the force calculated).

Answer 2

Well if you say "between two points" you don't need to multiply by anything or work out the components. The force from your formula is the force between to points along the line that connects them.