Quadrilateral EFGH is on a coordinate plane. Segment FG is on the line 2x − y = −3, and segment EH is on the line 2x − y = 1. Which statement proves how segments FG and EH are related?

Question

They have the same slope of 2 and are, therefore, parallel.
They have slopes that are opposite reciprocals of 1 and −1 and are, therefore, perpendicular.
They have slopes that are opposite reciprocals of 0 and undefined and are, therefore, perpendicular.
They have the same slope of −1 and are, therefore, parallel.

Answer 1

To analyze the relationship between segments FG and EH based on the lines they lie on, we first need to determine the slopes of these lines.

1. For the line \(2x - y = -3\):

   • Rearranging in slope-intercept form (y = mx + b): \[ -y = -2x - 3 \implies y = 2x + 3 \]
   • The slope (m) of this line is \(2\).

2. For the line \(2x - y = 1\):

   • Rearranging in slope-intercept form: \[ -y = -2x + 1 \implies y = 2x - 1 \]
   • The slope (m) of this line is also \(2\).

Since both lines have the same slope of \(2\), we can conclude that segments FG and EH are parallel.

Thus, the correct statement is: They have the same slope of 2 and are, therefore, parallel.