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Questions and Answers
What characteristic do parallel lines share?
What characteristic do parallel lines share?
How is the slope of a line that is perpendicular to another line determined?
How is the slope of a line that is perpendicular to another line determined?
What is the slope of a horizontal line?
What is the slope of a horizontal line?
If the slope of a line is 3, what is the slope of a line perpendicular to it?
If the slope of a line is 3, what is the slope of a line perpendicular to it?
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Which of the following lines is parallel to the line with slope 2?
Which of the following lines is parallel to the line with slope 2?
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What determines if a figure is a rectangle using slopes?
What determines if a figure is a rectangle using slopes?
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When determining if two lines are perpendicular, what specific characteristic must be true about their slopes?
When determining if two lines are perpendicular, what specific characteristic must be true about their slopes?
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What is the effect of changing the slope of a line on its parallel line?
What is the effect of changing the slope of a line on its parallel line?
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Study Notes
Slopes of Parallel and Perpendicular Lines
- Parallel lines: Streets parallel to 11th avenue are identified from the provided image.
- Perpendicular lines: Streets perpendicular to 11th avenue are identified from the image.
- Parallel lines (definition): When two lines have the same slope, they are considered parallel.
- Perpendicular lines (definition): When two lines have slopes that are negative reciprocals of each other, they are considered perpendicular.
- Horizontal lines and slopes: Horizontal lines have a slope of zero. The reciprocal of zero is undefined.
Identifying Parallel Lines (Example)
- Line GH: Passes through G(-4, 2) and H(2, -1).
- Line JK: Passes through J(-1, 7) and K(7, 3).
- Line MN: Passes through M(-4, 5) and N(5, 1).
- Parallel lines in the example? Determine if Line GH, JK, and MN are parallel, and justify your answer.
Examining Slopes to Compare Lines (Example)
- Line PQ: Passes through P(-7, 2) and Q(-2, 10).
- Line RS: Passes through R(-3, 4) and S(5, 1).
- Parallel, perpendicular, or neither? Determine if lines PQ and RS are parallel, perpendicular, or neither, justifying your answer.
- Sketching lines: Sketch the lines to verify your answer in part (a).
Using Slope to Identify a Polygon (Example)
- Polygon ABCD: ABCD is a parallelogram.
- Rectangle? Determine if ABCD is a rectangle using slopes. Justify the answer and explain how to use slopes to tell if a figure is a rectangle.
- Graph: The graph shows a parallelogram ABCD.
Identifying a Line Perpendicular to a Given Line (Example)
- Line EF: Passes through E(2, 3) and F(-1, -1).
- Slope of perpendicular line: Determine the slope of a line perpendicular to line EF.
- Coordinates of G: Find the coordinates of point G on a line perpendicular to line EF which passes through E(2,3).
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Description
This quiz explores the concepts of parallel and perpendicular lines through examples and definitions. You'll identify parallel lines from provided points and determine the slopes of various lines to assess their relationships. Test your understanding of lines and their slopes in this interactive exercise.
