Find the point that is 2/3 the way from a to b where
a(1, 4) and b(4,-8).

The coordinates of the point  M(x,y) = (3, -4)

Step-by-step explanation:

The coordinates of the point A  and B are A(1,4) and B(4,-8).

Let us assume the point which is 2/3 way on AB is m (x,y)

⇒ AM : AB  = 2 : 3, So, AM = 2 parts of total 3 parts.

⇒   AM: MB = 2 : 1   (as M is 2 - 3rd )

Now, using Section Formula:

Coordinates for point (x,y) which vides the line (a,b) and (c,d) in m1: m2 is given as

Applying this here on A(1,4) and B(4,-8) with m1: m2 = 2: 1

or, (x,y)  = (3,-4)

Hence  the coordinates of the point  M(x,y) = (3, -4)