Question

We all know the midpoint formula (I hope). For reference, here it is:
M_x=(x_2+x_1)/2, M_y=(x_2+x_1)/2
This is very useful for finding the midpoint, but I think it's limited. When I was in 10th grade, I made the following formula:
M_x=(x_2-x_1)*0.5+x_1, M_y=(y_2-y_1)*0.5+y_1
As it is, this does exactly the same thing - it finds the midpoint. However, you can alter the 0.5 to have it return the point x% of the way from point 1 to point 2. 0.1 would be 10%, 0.9 would be 90%, etc.
My question is, why isn't this taught in schools? I can't be the first person to have figured this out.

Answer 1

since midpoint is just the average of 2 points, there is no reason to teach how to find "not" the midpoint ....

now, if the question arises about some other point between two points that can be related in terms of percentages then yes; yours does aa fine job.

Answer 2

if you are figuring out how to apply what you know to what you dont, then kudos :) your actually using your brain rather than parroting rote memorizations