Coordinate Geometry
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Questions and Answers

What is the value of r in the polar coordinates of the point (3, 1)?

  • 3
  • 1
  • 4
  • 2 (correct)
  • In any triangle ABC, what is the condition for AB + BC > AC to be true?

  • AB = BC = CA
  • AB > BC > CA
  • AB ≠ BC ≠ CA
  • always true (correct)
  • What is the condition for a triangle ABC to be equilateral?

  • AB + BC > CA
  • AB = BC = CA (correct)
  • AB > BC > CA
  • AB ≠ BC ≠ CA
  • What is the formula for the area of a triangle in terms of its sides?

    <p>a² + b² - 2ab cos(θ)</p> Signup and view all the answers

    What is the condition for a quadrilateral ABCD to be a parallelogram?

    <p>AB = DC and AD = BC</p> Signup and view all the answers

    What is the point where the x-axis and y-axis intersect called?

    <p>Origin of coordinates</p> Signup and view all the answers

    What are the coordinates of the origin in a rectangular Cartesian coordinate system?

    <p>(0, 0)</p> Signup and view all the answers

    What is the coordinate of the orthocentre of a triangle with vertices (0, 3), (–3, 0) and (3, 0)?

    <p>(0, 3)</p> Signup and view all the answers

    If the coordinates of a point P are (x, y), what is the value of x if the point lies on the y-axis?

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

    If the centroid and circumcentre of a triangle are (3, 3) and (6, 2), what is the coordinate of the orthocentre?

    <p>(–3, 5)</p> Signup and view all the answers

    What is the formula to find the distance between two points P(x1, y1) and Q(x2, y2) in a rectangular Cartesian coordinate system?

    <p>PQ = √((x2 - x1)² + (y2 - y1)²)</p> Signup and view all the answers

    What is the formula for the area of a triangle with vertices A(x1, y1), B(x2, y2) and C(x3, y3)?

    <p>(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)) / 2</p> Signup and view all the answers

    If the polar coordinates of a point P are (r, θ), what is the value of y in terms of r and θ?

    <p>y = r sin θ</p> Signup and view all the answers

    What is the area of an equilateral triangle with side length 'a'?

    <p>(a^2 * sqrt(3)) / 4</p> Signup and view all the answers

    What is the formula for the area of a triangle with base 'b' and perpendicular height 'p'?

    <p>(b * p) / 2</p> Signup and view all the answers

    What is the condition for the points (0, 8/3), (1, 3), and (82, 30) to be collinear?

    <p>cos 2θ ≠ 1</p> Signup and view all the answers

    What is the effect of shifting the origin to a point (α, β) without rotation of axes?

    <p>The new equation of the curve is obtained by replacing x with x - α and y with y - β</p> Signup and view all the answers

    What is the result of rotating the axes without changing the origin?

    <p>The coordinates of the points remain unchanged</p> Signup and view all the answers

    What is the relationship between the vertices A, B, and C if AB + BC = AC?

    <p>The points A, B, and C are collinear</p> Signup and view all the answers

    What is the effect of shifting the origin on the equation of a curve?

    <p>The equation of the curve is transformed by replacing x with x + α and y with y + β</p> Signup and view all the answers

    What is the condition for the points A, B, and C to form an equilateral triangle?

    <p>AB = BC = CA</p> Signup and view all the answers

    What is the result of rotating the axes by 90 degrees without changing the origin?

    <p>The x-axis and y-axis are interchanged</p> Signup and view all the answers

    What is the relationship between the points A, B, and C if they are collinear?

    <p>AB + BC = AC</p> Signup and view all the answers

    What is the effect of shifting the origin on the coordinates of a point?

    <p>The coordinates of the point are translated by (α, β)</p> Signup and view all the answers

    What is the property of the points A, B, and C if they form a right-angled triangle?

    <p>AB^2 + BC^2 = CA^2</p> Signup and view all the answers

    If the centroid of a triangle ABC divides its median in the ratio k : 1, then what is the value of k?

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

    A line divides two points (2, -3) and (-5, 6) in the ratio 2:3 internally. What is the coordinate of the point of division?

    <p>(1, 2)</p> Signup and view all the answers

    If the vertices of a triangle are A(x1, y1), B(x2, y2), and C(x3, y3), then what are the coordinates of its centroid?

    <p>((x1+x2+x3)/3, (y1+y2+y3)/3)</p> Signup and view all the answers

    A line divides two points (1, 1) and (5, 7) in the ratio 3:4 internally. What is the equation of the line?

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

    If the ratio in which a line divides two points (x1, y1) and (x2, y2) is k:1, then what is the coordinate of the point of division?

    <p>((kx2 + x1)/(k + 1), (ky2 + y1)/(k + 1))</p> Signup and view all the answers

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