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Question 5 (1 point)
(04.02 MC)
Quadrilateral WXYZ is on a coordinate plane. Segment is on the line , and segment is on the line . Which statement proves
how segments and WZ are related?
a They have slopes that are opposite reciprocals of 1 and -1 and are, therefore, perpendicular.
d They have the same slope of 1 and are, therefore, parallel.
They have the same slope of -1 and are, therefore, parallel.
Thare opposite reciprocals of 0 and undefined and are, therefore, perpendicular.

Ask by Davies Page. in the United States
Jan 23,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

Segments and are parallel because they have the same slope of 1.

Solución

To determine the relationship between segments and :
  1. Find the slopes of the lines:
    • For on the line :
    • For on the line :
  2. Analyze the slopes:
    • Both lines have the same slope of 1.
  3. Conclusion:
    • Since and have identical slopes, they are parallel.
Correct Statement:
d. They have the same slope of 1 and are, therefore, parallel.
Answer: d They have the same slope of 1 and are, therefore, parallel.

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Extra Insights

When assessing the lines and , you can rewrite them in slope-intercept form, . For both lines, you’ll find that they have a slope of 1. Because they share the same slope, it proves that segments and are parallel—never intersecting, just like two well-behaved train tracks!
A common mistake is mistaking the slopes as being opposite reciprocals. When two lines have slopes that are equal, like in this case, they are parallel; however, lines with slopes that are true opposites, like 1 and -1, are perpendicular, meaning they intersect at a right angle. So, keep those definitions straight as you tackle more geometry problems!

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