Mathematics - Straight Lines
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Questions and Answers

What is the equation of the line parallel to the x-axis passing through the point (–2, 3)?

  • x = 3
  • x = –2
  • y = –2
  • y = 3 (correct)

    • What is the equation of the line parallel to the y-axis at a distance of –2 from the y-axis?

  • y = –2
  • x = 2
  • x = –2 (correct)
  • y = 2

    • In the point-slope form equation, what does 'm' represent?

  • The slope of the line (correct)
  • The intercept on the y-axis
  • The y-coordinate of the point
  • The x-coordinate of the point

    • Using the point-slope formula, what is the equation of the line with slope –4 that passes through (–2, 3)?

    <p>4x + y + 5 = 0</p> Signup and view all the answers

    Which relationship provides the slope between two points P1 (x1, y1) and P2 (x2, y2)?

    <p>y2 – y1 = m(x2 – x1)</p> Signup and view all the answers

    If the point-slope equation is given as y – y0 = m(x – x0), what does y0 represent?

    <p>The y-coordinate of the fixed point</p> Signup and view all the answers

    To find the equation of a line passing through points P1 (–1, 2) and P2 (1, 4), which formula is appropriate?

    <p>y – 2 = ((4 – 2)/(1 + 1))(x + 1)</p> Signup and view all the answers

    When determining the equation of a line in two-point form, what is the first step?

    <p>Identify the slope of the line</p> Signup and view all the answers

    How can you demonstrate that points (4, 4), (3, 5), and (–1, –1) form a right-angled triangle?

    <p>By calculating the slopes of the lines and showing they are perpendicular.</p> Signup and view all the answers

    What is the slope of a line that makes a 30° angle with the positive direction of the y-axis?

    <p>$\tan(30°)$</p> Signup and view all the answers

    For the points (x, –1), (2, 1), and (4, 5) to be collinear, what must be the value of x?

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

    How can it be shown that points (–2, –1), (4, 0), (3, 3), and (–3, 2) form a parallelogram?

    <p>By showing that opposite sides are parallel and equal in length.</p> Signup and view all the answers

    What is the angle between the x-axis and the line joining the points (3,–1) and (4,–2)?

    <p>30°</p> Signup and view all the answers

    If one line has a slope that is double that of another line, what can be inferred about the angles between them?

    <p>The tangent of the angle between them is a fixed ratio.</p> Signup and view all the answers

    If the points (h, 0), (a, b), and (0, k) lie on the same line, what relation must hold?

    <p>h + k = 1</p> Signup and view all the answers

    In which form can a horizontal line L at a distance 'a' from the x-axis be described?

    <p>Both A and C</p> Signup and view all the answers

    Study Notes

    Mathematics - Straight Lines

    • Right-angled Triangles: Points (4, 4), (3, 5), and (-1, -1) form a right-angled triangle. This can be proven without the Pythagorean theorem.

    • Slope of a Line: A line making a 30° angle with the positive y-axis has a specific slope.

    • Collinear Points: Finding the x-value that makes three points collinear (lie on the same line).

    • Parallelograms: Points (-2, -1), (4, 0), (3, 3), (-3, 2) define the vertices of a parallelogram, which can be shown without using distance formulas.

    • Angle Between Lines: The angle between the x-axis and a line segment connecting (3, -1) and (4, -2) must be calculated.

    • Slopes of Intersecting Lines: If one line's slope is double another and the tangent of the angle between them is 1/2. Calculate the slopes of the lines.

    • Point-Slope Formula: A line passing through (x₁, y₁) and (h, k) with slope m follows a specific equation: k - y₁ = m(h - x₁).

    • Points on a Line: If points lie on a line, 3 points (h,0), (a,b),(0,k) are collinear. It follows a condition.

    • Population Growth: A population graph (Fig 10.10) is given. Calculate the slope of the line AB and predict the population for the year 2010.

    Equation of a Line

    • Horizontal and Vertical Lines: Horizontal lines parallel to the x-axis follow equations y = a or y = -a (where 'a' is the distance from the x-axis). Vertical lines parallel to the y-axis follow equations x = b or x = -b (where 'b' is the distance from the y-axis).

    • Point-Slope Form: The equation of a line with slope 'm' passing through point (x₀, y₀) is given by y - y₀ = m(x - x₀).

    • Two-Point Form: The equation of a line passing through points (x₁, y₁) and (x₂, y₂) is y - y₁ = ((y₂-y₁)/(x₂-x₁)) * (x - x₁).

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    Mathematics Past Paper PDF - Straight Lines - 2021-22

    Description

    Test your understanding of straight lines in mathematics with this quiz. Topics include right-angled triangles, slopes of lines, and angles between intersecting lines. You'll also explore collinear points and parallelograms through practical problems.

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