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

`(AX)/(BX)=(YC)/(BY)`

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

`(BA-BX)/(10)=(YC)/(8)`

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

`(5)/(10)=(YC)/(8)`

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

`YC=8((5)/(10))`

Since

`(5)/(10)=(5\cdot1)/(5\cdot2)=(1)/(2)`

we have that

`\begin{gathered} YC=8((1)/(2)) \\ YC=(8)/(2) \\ YC=4 \end{gathered}`

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