Parallel & Perpendicular Lines
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Line A passes through points ( 0,9) and (6,5) Line B passes through points (-6,-3) and (0,-7) Are lines A and B parallel,perpendicular,or neither?
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Parallel
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Perpendicular
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Neither
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Explore the relationships between lines in this quiz titled 'Parallel & Perpendicular lines'. Assess your understanding of line equations, slopes, and geometric properties through problems involving coordinates and algebraic expressions. Essential for students enhancing their geometry skills.
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Line A passes through points ( 5,1) and (-2,6) Line B passes through points (-1,-1) and (5.5) Are lines A and B parallel,perpendicular,or neither?
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Parallel
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Perpendicular
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Neither
Correct Answer
A. NeitherExplanation
To determine if two lines are parallel, perpendicular, or neither, we need to compare their slopes. Line A has a slope of (6-1)/(-2-5) = -5/7. Line B has a slope of (-1-5.5)/(-1-5) = -6.5/-6 = 13/12. Since the slopes of the two lines are not equal, they are not parallel. Additionally, the product of their slopes (-5/7 * 13/12) is not equal to -1, so they are not perpendicular either. Therefore, the lines are neither parallel nor perpendicular.Rate this question:
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- 3.
Which equation is the equation of a line parallel to y = -3/5x + 6?
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Y = 5/3x + 3
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Y = -3/5x + 3
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Y = 5/3x + 6
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Y = 3/5x + 6
Correct Answer
A. Y = -3/5x + 3Explanation
The equation y = -3/5x + 3 is the equation of a line parallel to y = -3/5x + 6 because it has the same slope (-3/5) as the given equation. The y-intercept (3) is different, but this does not affect the parallel nature of the lines.Rate this question:
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- 4.
Which equation is the equation of a line perpendicular to y = 4/5x + 6 ?
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Y = -5/4x - 17
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Y = 5/4x + 6
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Y = 4/5x + 1
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Y = -4/5x - 2
Correct Answer
A. Y = -5/4x - 17Explanation
The equation of a line perpendicular to y = 4/5x + 6 would have a slope that is the negative reciprocal of 4/5. The negative reciprocal of 4/5 is -5/4. Therefore, the correct answer is y = -5/4x - 17.Rate this question:
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- 5.
Which equation is the equation of a line that is parallel to the x-axis and that passes through the point (-2, 5)?
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Y = 5x - 2
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Y = - 2
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Y = 5
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X = - 2
Correct Answer
A. Y = 5Explanation
The equation y = 5 represents a line that is parallel to the x-axis because the y-coordinate remains constant at 5 regardless of the value of x. This line passes through the point (-2, 5) as the y-coordinate is indeed 5 when x = -2.Rate this question:
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- 6.
Which equation is the equation of a line that is parallel to the y-axis and that passes through the point (7, -3)?
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X = 7
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Y = - 3
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Y = 7x - 3
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X = - 3
Correct Answer
A. X = 7Explanation
The equation x = 7 represents a vertical line that is parallel to the y-axis. This is because the value of x remains constant at 7, while the value of y can vary. Therefore, any point on this line will have an x-coordinate of 7. Since the equation passes through the point (7, -3), it satisfies the condition and is the correct answer.Rate this question:
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- 7.
Which equation is the equation of a line that is parallel to the line defined by y = -3x - 2 and that passes through the point (-2, -1)
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Y = -3x - 7
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Y = -3x + 5
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Y = 1/3x - 7
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Y = 1/3x + 5
Correct Answer
A. Y = -3x - 7Explanation
The equation y = -3x - 7 is the equation of a line that is parallel to the line defined by y = -3x - 2 because it has the same slope (-3). Additionally, it passes through the point (-2, -1) which satisfies the equation.Rate this question:
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- 8.
Which equation is the equation of a line tghat is perpendicular to the line defined by 4x - 5y - 12 = 0 with a y-intercept = - 2
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Y = 4/5x - 2
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Y = -4/5x - 2
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Y = -5/4x - 2
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Y = 5/4x - 2
Correct Answer
A. Y = -5/4x - 2Explanation
The equation of a line that is perpendicular to the line defined by 4x - 5y - 12 = 0 can be found by taking the negative reciprocal of the slope of the given line. The given line has a slope of 4/5, so the perpendicular line will have a slope of -5/4. The y-intercept remains the same, so the equation of the perpendicular line is y = -5/4x - 2.Rate this question:
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- 9.
Determine the equation of a line perpendicualr to -6x + 9y - 12 = 0 with the same y-intercept as the line defined by -8x + 2y - 6 = 0
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Y = 2/3x + 4/3
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Y = 2/3x + 3
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Y = -3/2x + 3
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Y = -3/2x + 4/3
Correct Answer
A. Y = -3/2x + 3Explanation
The given question asks for the equation of a line that is perpendicular to -6x + 9y - 12 = 0. To find the equation of a line perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line. The given line has a slope of 6/9, which simplifies to 2/3. The negative reciprocal of 2/3 is -3/2.
The question also states that the line should have the same y-intercept as the line defined by -8x + 2y - 6 = 0. To find the y-intercept of this line, we set x = 0 and solve for y. By doing this, we find that the y-intercept is 3.
Therefore, the equation of the line perpendicular to -6x + 9y - 12 = 0 with the same y-intercept as -8x + 2y - 6 = 0 is y = -3/2x + 3.Rate this question:
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- 10.
Determine the value of k in the graph
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-1
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-2
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-3
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-4
Correct Answer
A. -3Explanation
The value of k in the graph can be determined by looking at the position of the point on the y-axis. In this case, the point is located at -3 on the y-axis, so the value of k is -3.Rate this question:
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- 11.
Line A passes through points (-8,3) and (-6,7) Line B passes through points (-5,4) and (-3,3) Are lines A and B parallel, perpendicular, or neither?
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Parallel
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Perpendicular
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Neither
Correct Answer
A. NeitherExplanation
To determine whether lines A and B are parallel, perpendicular, or neither, we can examine the slopes of the lines.
For line A, the slope (m1) can be calculated as:
m1 = (y2 - y1) / (x2 - x1) = (7 - 3) / (-3 - (-8)) = 4 / 5
For line B, the slope (m2) can be calculated as:
m2 = (3 - 4) / (-3 - (-5)) = -1 / 2
Now, let's compare the slopes:
Lines A and B are neither parallel nor perpendicular because their slopes are not equal (not parallel) and the product of their slopes is not -1 (not perpendicular). They have different slopes, so they are neither parallel nor perpendicular to each other.Rate this question:
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Current Version
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Oct 17, 2023Quiz Edited by
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Aug 28, 2014Quiz Created by
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