Question

2) Given that XY || AC, what is YC if BX = 10, BA = 15, and BY = 8?A) 4 B) 6 C)8D)12

Answer 1

We can see that triangles ABC and AXY are congruent

This means that

$\frac{AX}{BX}=\frac{YC}{BY}$

Now, we know that BX=10, BY=8 and BA=AX+BX, hence AX=BA-BX, we have

$\frac{BA-BX}{10}=\frac{YC}{8}$

now, since BA-BX=15-10, BA-BX=5, it yields,

$\frac{5}{10}=\frac{YC}{8}$

Now, we need to isolate YC, this is given by

$YC=8(\frac{5}{10})$

Since

$\frac{5}{10}=\frac{5\cdot1}{5\cdot2}=\frac{1}{2}$

we have that

$\begin{gathered} YC=8(\frac{1}{2}) \\ YC=\frac{8}{2} \\ YC=4 \end{gathered}$

hence, the answer is YC=4, which corresponds to A).