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Questions and Answers
What is the equation of a line parallel to $y = 2x - 5$ that passes through the point (6, 8)?
What is the equation of a line parallel to $y = 2x - 5$ that passes through the point (6, 8)?
What is the equation of a line perpendicular to $y = 1/4x - 3$ that passes through the point (8, 2)?
What is the equation of a line perpendicular to $y = 1/4x - 3$ that passes through the point (8, 2)?
What can be concluded if the system of equations $y = 2x + 4$ and $3y - 6x = 12$ simplifies to a true statement 12 = 12?
What can be concluded if the system of equations $y = 2x + 4$ and $3y - 6x = 12$ simplifies to a true statement 12 = 12?
What is the equation of a line that runs perpendicular to $y = -3x + 2$ and passes through the point (-6, 0)?
What is the equation of a line that runs perpendicular to $y = -3x + 2$ and passes through the point (-6, 0)?
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What is one possible equation of a line parallel to $y = -2$ that passes through the point (7, 9)?
What is one possible equation of a line parallel to $y = -2$ that passes through the point (7, 9)?
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Are the planes AEB and IHC parallel or skew?
Are the planes AEB and IHC parallel or skew?
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Is plane ABE perpendicular to plane AEF?
Is plane ABE perpendicular to plane AEF?
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Which of the following represents skew lines?
Which of the following represents skew lines?
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Are planes CAE and GIE oblique planes?
Are planes CAE and GIE oblique planes?
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Which lines are described as parallel in the provided statements?
Which lines are described as parallel in the provided statements?
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Which statement correctly describes the relationship between lines CH and AJ?
Which statement correctly describes the relationship between lines CH and AJ?
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What is true regarding lines AB and BC?
What is true regarding lines AB and BC?
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Are lines AE and DC skew lines?
Are lines AE and DC skew lines?
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Are planes CBH and HIA perpendicular to each other?
Are planes CBH and HIA perpendicular to each other?
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How are lines DF and DE related?
How are lines DF and DE related?
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Study Notes
True or False Statements
- Plane AED is parallel to plane FGH: True
- Plane ABH is parallel to plane FCD: True
- Plane ABC is perpendicular to plane JFE: True
- Plane CBH is perpendicular to plane HIA: True
- Line AB and line HG are skew lines: True
- Line CG and line AI are skew lines: True
- Line AE and line BC are skew lines: True
- Line AB is parallel to line IH: False
- Line CF and line AJ are skew lines: True
- Line AD is parallel to line IF: True
- Line AB and line BC are oblique lines: True
- Line ED is parallel to line IG: True
- Line CH and line IJ are oblique lines: True
- Line AB is perpendicular to line AE: True
- Line AE and line AJ are oblique lines: True
- Line DF is perpendicular to line DE: True
- Plane CBH and plane HIA are oblique planes: True
- Plane CAF and plane GIE are oblique planes: True
Solving Systems of Equations
- System 1: x + 2y = 8, x - 2y = 4 has one solution: (6, 1)
- System 2: 2x + 3y = 12, 5x = 3y - 14 has one solution: (0, 4)
- System 3: x + 2y = 9, 3x + 2y = 7 has one solution: (-1,5)
- System 4: 2x + 3y = 7, 4x + 6y = 14 has infinitely many solutions.
Parallel and Perpendicular Lines
- Equation of a line parallel to y = 2x - 5 and passes through (6, 8): y = 2x - 4
- Equation of a line perpendicular to y = 2x - 5 and passes through (6, 8): y = -1/2x + 11
- Equation of a line parallel to y = 1/4x - 3 and passes through (8, 2): y = 1/4x - 1
- Equation of a line perpendicular to y = 1/4x - 3 and passes through (8, 2): y = -4x + 34
- Equation of a line parallel to y = -3x + 2 and passes through (-6, 0): y = -3x - 18
- Equation of a line perpendicular to y = -3x + 2 and passes through (-6, 0): y = 1/3x + 2
- Equation of a line parallel to y = -2 and passes through (7, 9): y = -2
- Equation of a line perpendicular to y = -2 and passes through (7, 9): x = 7
- Equation of a line parallel to 2x - y = 1 and passes through (-2, 6): y = 2x + 10
- Equation of a line perpendicular to 2x - y = 1 and passes through (-2, 6): y = -1/2x + 5
System of Equations Worked Example
- The given system has infinitely many solutions, as the substitution resulted in an equation that is always true.
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Description
Test your knowledge on geometric relationships involving planes and lines, as well as your ability to solve systems of equations. This quiz covers true or false statements about geometric properties and solutions to linear equations. Challenge yourself to see how well you understand these fundamental concepts!
