Question
Quadrilateral WXYZ is on a coordinate plane. Segment XY is on the line x − y = −3, and segment WZ is on the line x − y = 1. Which statement proves how segments XY and WZ are related?
They have slopes that are opposite reciprocals of 1 and −1 and are, therefore, perpendicular.
They have the same slope of 1 and are, therefore, parallel.
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.
Answers
GPT-4o mini
To determine the relationship between the segments XY and WZ, we need to find the slopes of the lines given by the equations they lie on.
1. The equation for segment XY is \(x - y = -3\). We can rewrite this in slope-intercept form (y = mx + b) as follows:
\[
y = x + 3
\]
This shows that the slope (m) of line XY is \(1\).
2. The equation for segment WZ is \(x - y = 1\). We can rewrite this in slope-intercept form as follows:
\[
y = x - 1
\]
This shows that the slope (m) of line WZ is also \(1\).
Since both segments XY and WZ have the same slope of \(1\), they are parallel.
Therefore, the correct statement that proves how segments XY and WZ are related is:
**They have the same slope of 1 and are, therefore, parallel.**
1. The equation for segment XY is \(x - y = -3\). We can rewrite this in slope-intercept form (y = mx + b) as follows:
\[
y = x + 3
\]
This shows that the slope (m) of line XY is \(1\).
2. The equation for segment WZ is \(x - y = 1\). We can rewrite this in slope-intercept form as follows:
\[
y = x - 1
\]
This shows that the slope (m) of line WZ is also \(1\).
Since both segments XY and WZ have the same slope of \(1\), they are parallel.
Therefore, the correct statement that proves how segments XY and WZ are related is:
**They have the same slope of 1 and are, therefore, parallel.**