Answer:
see explanation
Step-by-step explanation:
CY = CB + BY
= 6b + 5a - b
= 5a + 5b
---------------------
CX = CA + AX
= CA + [tex]\frac{1}{3}[/tex] AB , find AB
AB = AC + CB
= - 3a + 6b
= 6b - 3a
Thus
CX = CA + [tex]\frac{1}{3}[/tex] AB
= 3a + [tex]\frac{1}{3}[/tex](6b - 3a)
= 3a + 2b - a
= 2a + 2b
---------------------
and
[tex]\frac{2}{5}[/tex] CY
= [tex]\frac{2}{5}[/tex] (5a + 5b)
= 2a + 2b = CX
Hence CX = [tex]\frac{2}{5}[/tex] CY ⇒ Proven
