Question 6 (1 point) (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 \( A B \) 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

To determine the relationship between segments \( AB \) and \( CD \), we need to analyze the slopes of the lines on which these segments lie. 1. **Identify the slope of line \( AB \)**: The equation of line \( AB \) is given as: \[ y - 3 = 2(x + 2) \] This is in point-slope form, where the slope \( m_1 = 2 \). 2. **Identify the slope of line \( CD \)**: The equation of line \( CD \) is given as: \[ y - 3 = -\frac{1}{2}(x + 2) \] This is also in point-slope form, where the slope \( m_2 = -\frac{1}{2} \). 3. **Determine the relationship between the slopes**: - The slopes are \( m_1 = 2 \) and \( m_2 = -\frac{1}{2} \). - To check if the lines are perpendicular, we need to see if the product of the slopes equals \(-1\): \[ m_1 \cdot m_2 = 2 \cdot \left(-\frac{1}{2}\right) = -1 \] Since the product of the slopes is \(-1\), the lines are perpendicular. 4. **Conclusion**: The correct statement that proves the relationship of segments \( AB \) and \( CD \) is: - They are perpendicular because they have slopes that are opposite reciprocals of \( 2 \) and \( -\frac{1}{2} \). Thus, the answer is: **They are perpendicular because they have slopes that are opposite reciprocals of 2 and \( -\frac{1}{2} \).**