Section 5.5 - Parallel And Perpendicular Lines

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Section 5.5 - Parallel And Perpendicular Lines - Quiz

Complete the following questions


Questions and Answers
  • 1. 

    Which equation is the equation of a line parallel to y = -3/5x + 6?

    • A.

      Y = 5/3x + 3

    • B.

      Y = -3/5x + 3

    • C.

      Y = 5/3x + 6

    • D.

      Y = 3/5x + 6

    Correct Answer
    B. Y = -3/5x + 3
    Explanation
    The equation of a line that is parallel to y = -3/5x + 6 will have the same slope as -3/5. Therefore, the correct answer is y = -3/5x + 3 because it has the same slope of -3/5 as the original equation.

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  • 2. 

    Which equation is the equation of a line perpendicular to y = 4/5x + 6 ?

    • A.

      Y = -5/4x - 17

    • B.

      Y = 5/4x + 6

    • C.

      Y = 4/5x + 1

    • D.

      Y = -4/5x - 2

    Correct Answer
    A. Y = -5/4x - 17
    Explanation
    The equation y = -5/4x - 17 is the equation of a line perpendicular to y = 4/5x + 6 because the slopes of perpendicular lines are negative reciprocals of each other. The slope of y = 4/5x + 6 is 4/5, so the slope of the perpendicular line is -5/4. Additionally, the y-intercept of the perpendicular line is -17, which is different from the y-intercept of the original line. Therefore, y = -5/4x - 17 is the equation of a line perpendicular to y = 4/5x + 6.

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  • 3. 

    Determine which endpoints form a line that is parallel to the line segments with endpoints at P(4, 5) and Q(-3, 2)

    • A.

      M (2, 1) and N (-1, 8)

    • B.

      M (1, 2) and N (-6, -1)

    • C.

      M (4, 4) and N (-1, 1)

    • D.

      M (3, 5) and N (-3, 3)

    Correct Answer
    B. M (1, 2) and N (-6, -1)
    Explanation
    The line segments with endpoints at P(4, 5) and Q(-3, 2) have a slope of -1/7. In order for a line to be parallel to this line, it must have the same slope of -1/7. The line formed by the endpoints M (1, 2) and N (-6, -1) has a slope of -1/7, making it parallel to the given line segments. Therefore, M (1, 2) and N (-6, -1) form a line that is parallel to the line segments with endpoints at P(4, 5) and Q(-3, 2).

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  • 4. 

    Determine which endpoints form a line that is perpendicular to the line segments with endpoints at A(-2, -1) and B(6, -3)

    • A.

      C(3, 2) and D(7, -1)

    • B.

      C(-6, -4) and D(2, -6)

    • C.

      C(0, 0) and D(1, -4)

    • D.

      C(8, 7) and D(9, 11)

    Correct Answer
    D. C(8, 7) and D(9, 11)
    Explanation
    The line that is perpendicular to the line segment AB(-2, -1) and B(6, -3) will have a slope that is the negative reciprocal of the slope of AB. The slope of AB can be calculated as (change in y / change in x) = (-3 - (-1)) / (6 - (-2)) = -2/4 = -1/2. The negative reciprocal of -1/2 is 2. Therefore, the line that is perpendicular to AB will have a slope of 2. Looking at the given endpoints, the line formed by C(8, 7) and D(9, 11) will have a slope of (11 - 7) / (9 - 8) = 4/1 = 4, which is the negative reciprocal of -1/2. Hence, C(8, 7) and D(9, 11) form a line that is perpendicular to AB.

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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)?

    • A.

      Y = 5x - 2

    • B.

      Y = - 2

    • C.

      Y = 5

    • D.

      X = - 2

    Correct Answer
    C. Y = 5
    Explanation
    The equation y = 5 is the equation of a line that is parallel to the x-axis because it does not contain any term with x. This means that the value of x does not affect the value of y, and the line will be a horizontal line at y = 5. Additionally, the equation passes through the point (-2, 5) because when x = -2, y = 5. Therefore, the equation y = 5 satisfies both conditions of being parallel to the x-axis and passing through the point (-2, 5).

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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)?

    • A.

      X = 7

    • B.

      Y = - 3

    • C.

      Y = 7x - 3

    • D.

      X = - 3

    Correct Answer
    A. X = 7
    Explanation
    The equation of a line that is parallel to the y-axis will have a constant x-value. Since the line passes through the point (7, -3), the x-value must be 7. Therefore, the correct answer is x = 7.

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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)

    • A.

      Y = -3x - 7

    • B.

      Y = -3x + 5

    • C.

      Y = 1/3x - 7

    • D.

      Y = 1/3x + 5

    Correct Answer
    A. Y = -3x - 7
    Explanation
    The equation y = -3x - 7 is the equation of a line that is parallel to the line defined by y = -3x - 2. This is because the slope of both lines is -3, which means they have the same steepness. Additionally, the line y = -3x - 7 passes through the point (-2, -1), as required in the question. Therefore, this equation satisfies both conditions and is the correct answer.

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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

    • A.

      Y = 4/5x - 2

    • B.

      Y = -4/5x - 2

    • C.

      Y = -5/4x - 2

    • D.

      Y = 5/4x - 2

    Correct Answer
    C. Y = -5/4x - 2
    Explanation
    The equation of a line that is perpendicular to another line can be found by taking the negative reciprocal of the slope of the original line. The original 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.

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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

    • A.

      Y = 2/3x + 4/3

    • B.

      Y = 2/3x + 3

    • C.

      Y = -3/2x + 3

    • D.

      Y = -3/2x + 4/3

    Correct Answer
    C. Y = -3/2x + 3
    Explanation
    The equation of a line perpendicular to -6x + 9y - 12 = 0 will have a slope that is 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 line defined by -8x + 2y - 6 = 0 has a y-intercept of 3. Therefore, the line perpendicular to -6x + 9y - 12 = 0 with the same y-intercept will have an equation of y = -3/2x + 3.

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  • 10. 

    Determine the value of k in the graph

    • A.

      -1

    • B.

      -2

    • C.

      -3

    • D.

      -4

    Correct Answer
    C. -3
    Explanation
    The value of k in the graph is -3 because it is the only value that is shown in the given options.

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  • Current Version
  • Feb 02, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Oct 28, 2008
    Quiz Created by
    Seixeiroda
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