Question

question 15 (multiple choice worth 1 points) (04.02 mc) quadrilateral efch is on a coordinate plane. segment fg is on the line 3x - y = -2, and segment eh is on the 3x - y = -6. which statement proves how segments fg and eh are related? they have opposite reciprocals slopes of \\(\frac{1}{3}\\) and -3 and are, therefore, perpendicular. they have the same slope of \\(-\frac{1}{3}\\) and are, therefore, parallel. they have opposite reciprocal slopes of \\(-\frac{1}{3}\\) and 3 and are, therefore, perpendicular. they have the same slope of 3 and are, therefore, parallel.

Explanation:

Step1: Find slope of FG's line

The line for FG is \(3x - y=-2\). Rewrite in slope - intercept form \(y = mx + b\) (where \(m\) is slope).
\(y=3x + 2\), so slope \(m_1 = 3\).

Step2: Find slope of EH's line

The line for EH is \(3x - y=-6\). Rewrite in slope - intercept form:
\(y = 3x+6\), so slope \(m_2 = 3\).

Step3: Determine relationship

Parallel lines have the same slope. Since \(m_1=m_2 = 3\), the segments FG and EH (on these lines) are parallel.

Answer:

They have the same slope of 3 and are, therefore, parallel.