Answered

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

2 Given That XY AC What Is YC If BX 10 BA 15 And BY 8A 4 B 6 C8D12 class=

Sagot :

We can see that triangles ABC and AXY are congruent

This means that

[tex]\frac{AX}{BX}=\frac{YC}{BY}[/tex]

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

[tex]\frac{BA-BX}{10}=\frac{YC}{8}[/tex]

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

[tex]\frac{5}{10}=\frac{YC}{8}[/tex]

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

[tex]YC=8(\frac{5}{10})[/tex]

Since

[tex]\frac{5}{10}=\frac{5\cdot1}{5\cdot2}=\frac{1}{2}[/tex]

we have that

[tex]\begin{gathered} YC=8(\frac{1}{2}) \\ YC=\frac{8}{2} \\ YC=4 \end{gathered}[/tex]

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

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