Answer:
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 [tex](x,y) = (\frac{am2 + cm1}{m1+m2} ,\frac{dm1 + m2b}{m1+m2} )[/tex]
Applying this here on A(1,4) and B(4,-8) with m1: m2 = 2: 1
[tex](x,y) = (\frac{1(1) + 2(4)}{2+1} ,\frac{-8(2)+ 4(1)}{2+1} ) = (\frac{1+8}{3}, \frac{-16+4}{3} )\\\implies (x,y) = (\frac{9}{3} ,\frac{-12}{3} )[/tex]
or, (x,y) = (3,-4)
Hence the coordinates of the point M(x,y) = (3, -4)
