swerve wrote:What is the area of the triangle formed by the intersection of lines y=2x-2, y=-x/2 +8 and y=0?
A. 20
B. 30
C. 40
D. 45
E. 60
Source: Veritas Prep
\[? = {S_{\Delta {\text{ABC}}}}\]
\[{\text{point}}\,\,C\,\,\,\left\{ \begin{gathered}
\,y = 2x - 2\,\,\,\, \hfill \\
\,y = - \frac{x}{2} + 8\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,4} \,\,\,\,\,4y = - 2x + 32 \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,\,5y = 30\,\,\,\,\, \Rightarrow \,\,\,\,\,y = 6\,\,\,\,\,\,\,\left( { \Rightarrow \,\,\,\,\,x = 4} \right)\]
\[? = \frac{{AB \cdot CD}}{2} = \frac{{\left( {16 - 1} \right) \cdot 6}}{2} = 45\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
