If BX = 9 and BA = 15, we can say that the measure of AX = 6 because 15 - 9 = 6.
To solve the length of YC, we can have the following ratio:
[tex]\frac{BX}{XA}=\frac{BY}{YC}[/tex]
BX = 9, XA = 6, BY = 15, YC = x
Let's plug these values to the ratio above.
[tex]\frac{9}{6}=\frac{15}{x}[/tex]
Then, solve for x or the measure of YC.
[tex]\begin{gathered} \text{Cross multiply.} \\ 9x=90 \\ \text{Divide both sides by 9.} \\ \frac{9x}{9}=\frac{90}{9} \\ x=10 \end{gathered}[/tex]
Therefore, the measure of YC is 10 units.
