Mathematics 8 Transformations and Congruence
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Questions and Answers

Which transformation corresponds to a dilation with a scale factor of 3?

  • Reduction
  • Translation
  • Rotation
  • Enlargement (correct)
  • What is the scale factor indicating a reduction?

  • 3
  • 1.5
  • 0.5 (correct)
  • 2
  • What transformation sequence maps Figure A onto Figure B if the transformation type is a dilation followed by a translation?

  • Rotation then Dilation
  • Dilation then Translation (correct)
  • Translation then Rotation
  • Dilation then Reflection
  • If the scale factor is 0.93, what type of dilation is this?

    <p>Reduction</p> Signup and view all the answers

    What is the resulting scale factor when comparing a 20-inch wide screen to a 16-inch wide screen?

    <p>0.8</p> Signup and view all the answers

    When a figure is dilated with a scale factor of 1.000001, what happens to the figure?

    <p>It remains unchanged</p> Signup and view all the answers

    After performing a rotation of point G (4, 4) by 90° clockwise about the origin, what will be its new coordinates?

    <p>(-4, 4)</p> Signup and view all the answers

    What is the absolute value of the integer -5?

    <p>5</p> Signup and view all the answers

    What type of movement does the coordinate rule (𝑥, 𝑦) → (𝑥 + 10, 𝑦 + 8) represent?

    <p>Translation 10 units to the right and 8 units up</p> Signup and view all the answers

    When point A(-2, -10) is reflected over the x-axis, what are the new coordinates?

    <p>(2, 10)</p> Signup and view all the answers

    In a 90° clockwise rotation about the origin, what happens to the coordinates of point (x, y)?

    <p>(y, -x)</p> Signup and view all the answers

    Which statement about triangle DEF rotated 90° clockwise about the origin is TRUE?

    <p>The triangle remains congruent after rotation</p> Signup and view all the answers

    What transformation is used to move figure A to figure B if figure B is identical to figure A?

    <p>No transformation needed</p> Signup and view all the answers

    Which of the following describes the movement not included in the set of transformations?

    <p>Scaling</p> Signup and view all the answers

    If triangle DEF has vertices D(0,0), E(3,0), and F(3,4), what will be the coordinates of the vertices after a reflection over the y-axis?

    <p>D(0,0), E(-3,0), F(-3,4)</p> Signup and view all the answers

    What is the value of x in the equation 𝑥 + 5 = 12?

    <p>7</p> Signup and view all the answers

    What is the solution to the equation 3𝑥 = 18?

    <p>6</p> Signup and view all the answers

    Which angles are classified as Alternate Interior Angles?

    <p>∠4 and ∠6</p> Signup and view all the answers

    For the equation 𝑥 - 4 = 10, what is the value of x?

    <p>14</p> Signup and view all the answers

    What is the slope between the points (0, 0) and (2, 4)?

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

    Which of the following options correctly represents the equation of a line with a slope of -1?

    <p>y = -x</p> Signup and view all the answers

    If 𝑥 + 9 = 20, what is the value of x?

    <p>10</p> Signup and view all the answers

    What is the value of angle 3 if it complements angle 4 to 90°?

    <p>35°</p> Signup and view all the answers

    In the slope-intercept form, what does 'm' represent?

    <p>The slope</p> Signup and view all the answers

    If the line passes through points (2, -4) and (4, -8), what is the slope?

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

    For the equation 7𝑥 - 3𝑥 - 8 = 24, what is the value of x?

    <p>8</p> Signup and view all the answers

    What is the solution to the equation $x + 4 = 10$?

    <p>6</p> Signup and view all the answers

    What is the correct way to solve the equation 𝑥 = 4?

    <p>x = 2 + 2</p> Signup and view all the answers

    Which angles are Corresponding Angles?

    <p>∠3 and ∠6</p> Signup and view all the answers

    What is the equation of the line that passes through points (1, 0) and (3, 4)?

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

    Which equation has no solution?

    <p>$x + 1 = x - 1$</p> Signup and view all the answers

    What is the solution to the equation $5x = 25$?

    <p>5</p> Signup and view all the answers

    Which of the following equations has one solution?

    <p>$3x - 4 = 2x + 6$</p> Signup and view all the answers

    What is the solution to the equation $2(x - 3) = 2x - 6$?

    <p>Infinitely many solutions</p> Signup and view all the answers

    What type of angles are formed when parallel lines are cut by a transversal?

    <p>Alternate interior angles</p> Signup and view all the answers

    Which of the following pairs are vertical angles?

    <p>Angles that are opposite each other when two lines intersect</p> Signup and view all the answers

    What are the coordinates of 𝑀′ when 𝑀(−8, 4) is reflected over the 𝑥-axis?

    <p>(−8, −4)</p> Signup and view all the answers

    Which of the following transformations can map quadrilateral 𝐵𝐼𝐾𝐸 onto quadrilateral 𝐺𝑂𝐿𝐹?

    <p>Reflect over the x-axis then translate</p> Signup and view all the answers

    What is the value of 𝑥 in the equation $5x = 100$?

    <p>$x = 20$</p> Signup and view all the answers

    Which value of 𝑥 satisfies the equation $10x - 2x - 2 = 22$?

    <p>$x = 3$</p> Signup and view all the answers

    Which equation correctly reflects the statement: 𝑥 + 3 = 12?

    <p>The value of 𝑥 is 9.</p> Signup and view all the answers

    What should follow after reflecting quadrilateral 𝐵𝐼𝐾𝐸?

    <p>Translate quadrilateral 𝐵𝐼𝐾𝐸 vertically</p> Signup and view all the answers

    In the context of solving equations, which statement is true about the equation $5x = 15$?

    <p>The value of 𝑥 is 3.</p> Signup and view all the answers

    Study Notes

    Mathematics Worksheets

    • Subjects: Mathematics 8
    • Lesson Titles: Investigate Transformations, Understand and Recognize Congruent Figures, Explore Parallel Lines Cut by a Transversal, Derive y = mx, Solve Multi-step Linear Equations, Examine Special Cases, Develop Angle Relationships for Triangles
    • Worksheet Numbers: 1 through 9
    • Dates: Various dates throughout September and October, 2024
    • Teacher: Mr. Kristoffer
    • Instructions: Students are on a mission to find a treasure by completing levels of math worksheets. They are to level up by completing the worksheet problems.
    • Assessment Types: Worksheets, quizzes, and problem-solving activities
    • Concepts Covered: Coordinate transformations (slides, flips, turns), reflections, rotations, translations, dilations, congruent figures, linear equations, solving multi-step equations, special cases in equations, triangle angle relationships, and angle properties of parallel lines.
    • Materials: Graph paper, rulers, protractors (possibly).

    Specific Worksheet Details

    • Worksheet A (Climb the Mountain): Focuses on finding opposite values and absolute values of integers and describing movements of figures.
    • Worksheet L (Swim the Ocean): Multi-choice questions about transformations in the coordinate plane and finding measures of angles related to triangles, parallels, and transversals.
    • Worksheet IA (Grab the Treasure): problem-solving questions on transformations.
    • Quizzes: Assessment of understanding of course material in a quiz format.
    • Table use: Students use tables to record information about transformations and reflections in some worksheets.

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    Description

    Join Mr. Kristoffer's class on a treasure quest by completing various math worksheets covering transformations, congruent figures, linear equations, and triangle angle relationships. Each worksheet will challenge you with exciting problems that require problem-solving skills and critical thinking. Are you ready to level up your math skills?

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