Geometry: Properties of Perpendicular Lines
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Questions and Answers

Which of the following statements about lines m and k is true given they are perpendicular?

  • The slopes of lines m and k are equal in magnitude.
  • Line m and line k do not intersect.
  • Line m and line k have the same slope.
  • The product of the slopes of lines m and k is -1. (correct)

    • When lines m and k intersect, what is the sum of their slopes?

  • 2
  • -1
  • 0 (correct)
  • 1

    • If line m is perpendicular to line k, which of the following statements could be true?

  • Line m and line k intersect. (correct)
  • Line m and line k run parallel to each other.
  • The slopes of lines m and k are both positive.
  • Line m creates an obtuse angle at the intersection with line k.

    • Which of these characteristics does NOT apply to perpendicular lines m and k?

    <p>They have slopes that are positive.</p> Signup and view all the answers

    What can be inferred about the angle created by line m at the intersection with line k?

    <p>It must be a right angle.</p> Signup and view all the answers

    Which statement is true regarding two lines in the same plane that do not intersect?

    <p>The lines must be parallel.</p> Signup and view all the answers

    Is it true that if two lines in space do not intersect, they must be parallel?

    <p>No, they might be skew lines.</p> Signup and view all the answers

    Which statement is correct regarding parallel lines?

    <p>If lines are parallel, they must lie in the same plane.</p> Signup and view all the answers

    What can be concluded about two lines that are parallel?

    <p>They may be skew to another line.</p> Signup and view all the answers

    Which of the following statements is incorrect?

    <p>Lines in space that do not intersect are parallel.</p> Signup and view all the answers

    Which statement is true regarding points J, K, and L?

    <p>J, K, and L are coplanar.</p> Signup and view all the answers

    What can be said about the segments JK and KL?

    <p>JK is equal to KL.</p> Signup and view all the answers

    Which of the following cannot be concluded based on JK = KL?

    <p>K is the midpoint of JL.</p> Signup and view all the answers

    If J, K, and L are coplanar, which of the following must also be true?

    <p>Intervals JK and KL are equal.</p> Signup and view all the answers

    Which statement is NOT a necessary conclusion based on JK = KL?

    <p>K is the midpoint of JL.</p> Signup and view all the answers

    Which statement about lines in the same plane is true?

    <p>If two lines do not intersect, they must be parallel.</p> Signup and view all the answers

    Which statement regarding lines in space is correct?

    <p>If two lines do not intersect, they may be skew lines.</p> Signup and view all the answers

    What can be concluded if two lines are parallel?

    <p>They must lie in the same plane.</p> Signup and view all the answers

    Which of the following options is incorrect regarding non-intersecting lines?

    <p>Non-intersecting lines in the same plane must be skew.</p> Signup and view all the answers

    What is false about lines that are parallel?

    <p>They can be in different planes.</p> Signup and view all the answers

    What is the slope of the longer base of the trapezoid?

    <p>$ rac{2}{3}$</p> Signup and view all the answers

    Which point is used to find the equation of the line containing the shorter base?

    <p>(3, 1)</p> Signup and view all the answers

    Using the point-slope form, which equation represents the line containing the shorter base before simplification?

    <p>$y - 1 = \frac{2}{3}(x - 3)$</p> Signup and view all the answers

    What is the final equation of the line containing the shorter base after simplification?

    <p>$y = \frac{2}{3}x - 1$</p> Signup and view all the answers

    If the slope of both bases of a trapezoid is equal, what can be inferred about their lines?

    <p>They are parallel to each other.</p> Signup and view all the answers

    What is the slope of the longer base of the trapezoid?

    <p>2/3</p> Signup and view all the answers

    Which equation correctly represents the shorter base of the trapezoid?

    <p>y = rac{2}{3}x - 1</p> Signup and view all the answers

    Given the point (3, 1) on the shorter base, which form of the equation was used to derive its line equation?

    <p>Point-slope form</p> Signup and view all the answers

    What characteristic do the bases of a trapezoid share?

    <p>They are parallel to each other.</p> Signup and view all the answers

    What is the vertical intercept of the shorter base's line equation $y = rac{2}{3}x - 1$?

    <p>-1</p> Signup and view all the answers

    What is the result of reflecting rectangle PQRS across the x-axis?

    <p>Rectangle P'Q'R'S' is formed.</p> Signup and view all the answers

    What is necessary to transform rectangle P'Q'R'S' back to PQRS after reflecting across the x-axis?

    <p>A reflection across the y-axis followed by a 180° rotation around the origin.</p> Signup and view all the answers

    Which transformation would NOT return rectangle P'Q'R'S' to rectangle PQRS?

    <p>Two consecutive reflections across the x-axis.</p> Signup and view all the answers

    After rectangle PQRS is reflected across the x-axis, which point changes its coordinates from (x, y) to (x, -y)?

    <p>(x1, y1)</p> Signup and view all the answers

    Which transformation sequence describes a method to transform rectangle PQRS back from its reflection P'Q'R'S'?

    <p>Reflection across the y-axis followed by a 180° rotation around the origin.</p> Signup and view all the answers

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