find the coodinates of the point 4/5 of the way from b to a

Question

b is (13,11)

a is (3, -4)

Answer 1

There is a neat trick for constructing a line segment from b to a, using a variable t, as follows:

ba = (1-t)*b + t*a, 0 <= t <= 1.

As t varies from 0 to one, we move from b to a in a straight line.

So, for me to be 4/5 of the way from b to a, I simply let t = 4/5 in this equation.

Now, calculate (1-4/5)*b + (4/5)*a.