Coordinate Geometry

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?

a² + b² - 2ab cos(θ) (C) Signup and view all the answers

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

AB = DC and AD = BC (C) Signup and view all the answers

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

Origin of coordinates (D) Signup and view all the answers

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

(0, 0) (B) 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)?

(0, 3) (A) 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?

x = 0 (A) 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?

(–3, 5) (B) 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?

PQ = √((x2 - x1)² + (y2 - y1)²) (C) 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)?

(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)) / 2 (B) 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?

y = r sin θ (B) Signup and view all the answers

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

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

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

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

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

cos 2θ ≠ 1 (D) Signup and view all the answers

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

The new equation of the curve is obtained by replacing x with x - α and y with y - β (B) Signup and view all the answers

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

The coordinates of the points remain unchanged (B) Signup and view all the answers

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

The points A, B, and C are collinear (B) Signup and view all the answers

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

The equation of the curve is transformed by replacing x with x + α and y with y + β (D) Signup and view all the answers

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

AB = BC = CA (B) Signup and view all the answers

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

The x-axis and y-axis are interchanged (A) Signup and view all the answers

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

AB + BC = AC (C) Signup and view all the answers

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

The coordinates of the point are translated by (α, β) (A) Signup and view all the answers

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

AB^2 + BC^2 = CA^2 (A) 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?

2 (C) 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?

(1, 2) (A) 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?

((x1+x2+x3)/3, (y1+y2+y3)/3) (D) 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?

x + y = 4 (C) 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?

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