Straight Line
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Questions and Answers

What is the equation of the bisector of the acute angle between the lines 3x - 4y + 7 = 0 and 12x + 5y - 2 = 0?

  • 3x + 4y - 7 = 0
  • 21x + 77y - 101 = 0
  • 12x - 5y + 2 = 0
  • 11x - 3y + 9 = 0 (correct)

    • What is the length of the perpendicular from the origin to the line ax + by + c = 0?

  • x1 cos α + y1 sin α - p
  • |ax1 + by1 + c| / √(a^2 + b^2) (correct)
  • α / (a^2 + b^2)
  • √(a^2 + b^2)

    • What is the distance of a point (x1, y1) from the line ax + by + c = 0?

  • x1 cos α + y1 sin α - p
  • |ax1 + by1 + c| / √(a^2 + b^2) (correct)
  • √(a^2 + b^2)
  • α / (a^2 + b^2)

    • What is the equation of two parallel lines?

    <p>ax + by + c1 = 0 and ax + by + c2 = 0</p> Signup and view all the answers

    What is the slope of a line perpendicular to the line 3x - 4y + 7 = 0?

    <p>-4/3</p> Signup and view all the answers

    What is the slope of a line parallel to the x-axis?

    <p>0</p> Signup and view all the answers

    What is the condition for two lines to be parallel?

    <p>Slopes are equal</p> Signup and view all the answers

    What is the slope of a line that is equally inclined with the axes?

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

    How many points determine a unique line?

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

    What is the slope of a line perpendicular to another line with a slope of 2?

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

    What is the equation of the line bisecting perpendicularly the segment joining the points (–4, 6) and (8, 8)?

    <p>6x + y - 19 = 0</p> Signup and view all the answers

    What is the slope of the line passing through (–4, 6) and (8, 8)?

    <p>1/4</p> Signup and view all the answers

    What is the midpoint of the line segment joining the points (–4, 6) and (8, 8)?

    <p>(2, 7)</p> Signup and view all the answers

    What is the equation of a line parallel to the line passing through (–4, 6) and (8, 8)?

    <p>y - 7 = 1/4(x - 2)</p> Signup and view all the answers

    What is the equation of a line perpendicular to the line passing through (–4, 6) and (8, 8)?

    <p>x + 4y - 7 = 0</p> Signup and view all the answers

    If a line passes through the points (–4, 6) and (8, 8), what is the equation of a line perpendicular to it?

    <p>6x – 2y + 19 = 0</p> Signup and view all the answers

    What is the midpoint of the line segment joining the points (5, 3) and (9, 11)?

    <p>(7, 7)</p> Signup and view all the answers

    If two lines have slopes of 3/4 and –4/3, what can be said about the lines?

    <p>They are perpendicular</p> Signup and view all the answers

    What is the equation of a line that passes through the point (3, 4) and is parallel to the line 2x + 3y – 7 = 0?

    <p>2x + 3y + 5 = 0</p> Signup and view all the answers

    What is the slope of a line that is perpendicular to the line x + 2y – 5 = 0?

    <p>1/–2</p> Signup and view all the answers

    If the lines 3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 are intersecting, what is the tangent of the angle between them?

    <p>13/35</p> Signup and view all the answers

    What is the equation of the line parallel to the line 3x - 4y + 7 = 0 and passing through the point (1, 1)?

    <p>3x - 4y - 2 = 0</p> Signup and view all the answers

    If the length of the perpendicular from the origin to the line ax + by + c = 0 is p, what is the value of $\frac{a^2+b^2}{p^2}$?

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

    What is the midpoint of the line segment joining the points (3, 4) and (5, 8)?

    <p>(4, 6)</p> Signup and view all the answers

    What is the slope of the line perpendicular to the line 3x - 4y + 7 = 0?

    <p>-3/4</p> Signup and view all the answers

    If a line passes through the points A(x1, y1) and B(x2, y2), what is the slope of the line?

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

    What is the equation of a line perpendicular to the line ax + by + c = 0?

    <p>bx - ay + c = 0</p> Signup and view all the answers

    If two lines have slopes m1 and m2, what is the condition for them to be perpendicular?

    <p>m1 = -m2</p> Signup and view all the answers

    What is the midpoint of the line segment joining the points (x1, y1) and (x2, y2)?

    <p>((x1 + x2)/2, (y1 + y2)/2)</p> Signup and view all the answers

    What is the equation of a line parallel to the line ax + by + c = 0?

    <p>ax + by + kc = 0, where k is a constant</p> Signup and view all the answers

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