\begin{tabular}{l} Question 9 (Multiple Choice Worth 1 points) \\ (04.02 MC) \\ Segment AB is on the line \( y-3=2(x+2) \), and segment CD is on the line \( y-3=-\frac{1}{2}(x+2) \). Which statement proves the relationship of segments AB and CD? \\ They are parallel because they have the same slope of 2 . \\ They are parallel because they have the same slope of \( -\frac{1}{2} \). \\ They are perpendicular because they have slopes that are opposite reciprocals of 2 and \( -\frac{1}{2} \). \\ They are perpendicular because they have slopes that are opposite reciprocals of -2 and \( \frac{1}{2} \). \\ Ther \\ Ther \\ \hline\end{tabular}

Both lines in the question can be analyzed to understand their slopes better. The line \( y-3=2(x+2) \) has a slope of 2, while the line \( y-3=-\frac{1}{2}(x+2) \) has a slope of \(-\frac{1}{2}\). When slopes are negative reciprocals of each other (like 2 and \(-\frac{1}{2}\)), it means the lines are perpendicular. So, the correct answer would state that they are perpendicular due to their opposing slope relationships. To visualize this concept in real-life, think of how two ramps meet at a right angle. If one ramp rises up steeply, like the line with slope 2, the other must descend slowly and steadily, just like the line with slope \(-\frac{1}{2}\). This real-world connection helps to reaffirm why perpendicular lines intersect to form that signature right-angle we've come to recognize.