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Quadrilateral [tex]WXYZ[/tex] is on a coordinate plane. Segment [tex]XY[/tex] is on the line [tex]x - y = -3[/tex], and segment [tex]WZ[/tex] is on the line [tex]x - y = 1[/tex].

Which statement proves how segments [tex]XY[/tex] and [tex]WZ[/tex] are related?

A. They have slopes that are opposite reciprocals of 1 and -1 and are, therefore, perpendicular.
B. They have the same slope of 1 and are, therefore, parallel.
C. They have slopes that are opposite reciprocals of 0 and undefined and are, therefore, perpendicular.
D. They have the same slope of -1 and are, therefore, parallel.



Answer :

GinnyAnswer
To determine the relationship between the segments [tex]\(XY\)[/tex] and [tex]\(WZ\)[/tex] based on their slopes, we need to analyze the given lines [tex]\(x - y = -3\)[/tex] and [tex]\(x - y = 1\)[/tex].

1. Identify Line Equations and Their Forms:
- The equation of line [tex]\(XY\)[/tex] is given by [tex]\(x - y = -3\)[/tex].
- The equation of line [tex]\(WZ\)[/tex] is given by [tex]\(x - y = 1\)[/tex].

2. Rewrite in Slope-Intercept Form:
- The slope-intercept form of a line is [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope.
- Rewrite [tex]\(x - y = -3\)[/tex] as [tex]\(y = x + 3\)[/tex]. Thus, the slope of line [tex]\(XY\)[/tex] is [tex]\(1\)[/tex].
- Rewrite [tex]\(x - y = 1\)[/tex] as [tex]\(y = x - 1\)[/tex]. Thus, the slope of line [tex]\(WZ\)[/tex] is [tex]\(1\)[/tex].

3. Compare the Slopes:
- The slope of line [tex]\(XY\)[/tex] is [tex]\(1\)[/tex].
- The slope of line [tex]\(WZ\)[/tex] is [tex]\(1\)[/tex].

4. Determine Relationship:
- Since the slopes of both lines (segments) are equal (both are [tex]\(1\)[/tex]), the lines are parallel.

5. Conclusion:
- Therefore, the segments [tex]\(XY\)[/tex] and [tex]\(WZ\)[/tex] have the same slope of [tex]\(1\)[/tex] and are parallel.

The correct statement that proves how segments [tex]\(XY\)[/tex] and [tex]\(WZ\)[/tex] are related is:
- They have the same slope of 1 and are, therefore, parallel.

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