Coordinate Geometry

1. What is the x-coordinate of a point called?
  a) Ordinate
  b) Abscissa
  c) Distance
  d) Slope
  Answer: b
2. What is the distance of a point from the x-axis called?
  a) Slope
  b) Radius
  c) Ordinate
  d) Abscissa
  Answer: c
3. The coordinates of a point on the x-axis are in which form?
  a) (x, 0)
  b) (0, y)
  c) (x, y)
  d) (y, x)
  Answer: a
4. Which theorem is used to calculate the distance between two points?
  a) Pythagoras Theorem
  b) Triangle Theorem
  c) Midpoint Theorem
  d) Ratio Theorem
  Answer: a
5. What is the distance formula between two points P(x₁, y₁) and Q(x₂, y₂)?
  a) √((x₂-x₁)² – (y₂-y₁)²)
  b) √((x₂-x₁)² + (y₂-y₁)²)
  c) √((x₂-x₁)² * (y₂-y₁)²)
  d) √((x₁+x₂)² + (y₁+y₂)²)
  Answer: b
6. What is the distance of a point (x, y) from the origin?
  a) √(x² + y²)
  b) √(x² – y²)
  c) √(x² + y)
  d) √(x – y²)
  Answer: a
7. A point equidistant from two points lies on the _______.
  a) Perpendicular Bisector
  b) Median
  c) Altitude
  d) Axis
  Answer: a
8. The coordinates of a point dividing a line segment in the ratio m₁:m₂ internally is given by:
  a) ((m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂))
  b) ((m₁x₁ + m₂x₂)/(m₁ + m₂), (m₁y₂ – m₂y₁)/(m₁ + m₂))
  c) ((m₁x₂ – m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂))
  d) ((m₁x₂ + m₂x₁)/(m₁ – m₂), (m₁y₂ + m₂y₁)/(m₁ – m₂))
  Answer: a
9. What is the ratio in which the midpoint of a line segment divides it?
  a) 2:1
  b) 1:1
  c) 3:1
  d) 1:2
  Answer: b
10. The midpoint formula for a line joining P(x₁, y₁) and Q(x₂, y₂) is:
  a) ((x₁ – x₂)/2, (y₁ – y₂)/2)
  b) ((x₁ + x₂)/2, (y₁ + y₂)/2)
  c) ((x₁x₂)/2, (y₁y₂)/2)
  d) ((x₁ – x₂)/2, (y₁ + y₂)/2)
  Answer: b
11. A triangle with one angle as 90° is called:
  a) Isosceles triangle
  b) Equilateral triangle
  c) Right triangle
  d) Scalene triangle
  Answer: c
12. If two points A and B lie on the x-axis, their y-coordinates are:
  a) Positive
  b) Negative
  c) Zero
  d) Undefined
  Answer: c
13. The length of the diagonal of a square is given by:
  a) Side²
  b) Side√2
  c) 2*Side
  d) √(Side)
  Answer: b
14. The line segment joining (4, -3) and (8, 5) is divided in a ratio of 3:1. The coordinates of the dividing point are:
  a) (7, 3)
  b) (6, 2)
  c) (5, 0)
  d) (4, 1)
  Answer: a
15. What type of figure is formed if all four sides are equal and the diagonals bisect each other?
  a) Rectangle
  b) Parallelogram
  c) Square
  d) Trapezium
  Answer: c
16. The distance of a point P(x, y) from the origin O(0, 0) is represented as:
  a) OP = √(x² + y²)
  b) OP = √(x² – y²)
  c) OP = √(x + y)
  d) OP = √(x – y)
  Answer: a
17. The sum of the angles of a triangle is always:
  a) 360°
  b) 180°
  c) 90°
  d) 270°
  Answer: b
18. A line joining (3, 4) and (-3, -4) is divided by the y-axis in which ratio?
  a) 1:1
  b) 2:1
  c) 3:1
  d) 5:1
  Answer: d
19. The point (0, 5) lies on:
  a) X-axis
  b) Y-axis
  c) Both axes
  d) None of these
  Answer: b
20. What is the name of the point that divides a segment externally?
  a) Interior point
  b) Exterior point
  c) Sectional point
  d) Centroid
  Answer: b
21. A triangle is said to be collinear if:
  a) The sum of two sides is equal to the third side
  b) All angles are 60°
  c) All points lie on the same line
  d) The area is zero
  Answer: d
22. If a line segment is trisected, it is divided into:
  a) 2 equal parts
  b) 3 equal parts
  c) 4 equal parts
  d) 5 equal parts
  Answer: b
23. Which formula is used to find the area of a triangle given three vertices?
  a) Distance formula
  b) Section formula
  c) Shoelace formula
  d) Heron’s formula
  Answer: c
24. A point on the x-axis is of the form:
  a) (0, x)
  b) (x, 0)
  c) (x, y)
  d) (y, 0)
  Answer: b
25. The distance between points A(0, 0) and B(3, 4) is:
  a) 5 units
  b) 7 units
  c) 6 units
  d) 9 units
  Answer: a
26. A quadrilateral whose opposite sides are equal is called:
  a) Square
  b) Rectangle
  c) Parallelogram
  d) Rhombus
  Answer: c
27. What is the slope of a vertical line?
  a) 1
  b) 0
  c) Undefined
  d) Negative
  Answer: c
28. A point lies on the line x + y = 5. What relation must x and y satisfy?
  a) x = y
  b) x – y = 5
  c) x + y = 5
  d) x² + y² = 5
  Answer: c
29. In coordinate geometry, the perpendicular bisector is equidistant from:
  a) All points on the line segment
  b) The origin
  c) The endpoints of the segment
  d) The x-axis
  Answer: c
30. If the vertices of a parallelogram are A, B, C, and D, then its diagonals:
  a) Are equal
  b) Bisect each other
  c) Are parallel
  d) Are perpendicular
  Answer: b
31. The distance between points (1, 1) and (4, 5) is:
  a) √25
  b) 5
  c) √18
  d) 4
  Answer: b
32. A point equidistant from (3, 4) and (7, 8) lies on:
  a) The x-axis
  b) The y-axis
  c) The perpendicular bisector of the line joining the two points
  d) The line x = y
  Answer: c
33. What is the slope of the line joining (2, 3) and (6, 7)?
  a) 1
  b) 2
  c) 3
  d) 0
  Answer: a
34. A triangle has vertices A(0, 0), B(4, 0), and C(0, 3). The area of the triangle is:
  a) 6 square units
  b) 12 square units
  c) 7 square units
  d) 10 square units
  Answer: a
35. The point (0, -5) lies:
  a) On the x-axis
  b) On the y-axis
  c) In the first quadrant
  d) In the second quadrant
  Answer: b
36. The slope of a horizontal line is:
  a) 1
  b) 0
  c) Undefined
  d) Infinite
  Answer: b
37. A line passing through the origin has an equation of the form:
  a) x = y
  b) y = mx
  c) x + y = 0
  d) y = c
  Answer: b
38. The coordinates of the centroid of a triangle are:
  a) The average of the midpoints
  b) The average of the vertices’ coordinates
  c) The intersection of medians
  d) None of the above
  Answer: b
39. A square is a special type of:
  a) Parallelogram
  b) Trapezium
  c) Rectangle
  d) Both a and c
  Answer: d
40. What is the equation of a line parallel to the x-axis?
  a) x = 0
  b) y = constant
  c) x = constant
  d) y = 0
  Answer: b
41. The diagonal of a rhombus divides it into:
  a) Four triangles of equal area
  b) Two triangles of equal area
  c) Four congruent triangles
  d) None of the above
  Answer: a
42. The length of the side of a square whose diagonal is 10√2 is:
  a) 10
  b) 20
  c) 5
  d) 10√2
  Answer: a
43. The vertices of a triangle are A(1, 2), B(3, 6), and C(5, 2). The base BC is:
  a) 5 units
  b) 4 units
  c) 6 units
  d) 7 units
  Answer: b
44. If a point divides a segment externally, the section formula uses:
  a) Positive ratios
  b) Negative ratios
  c) Reciprocal ratios
  d) Undefined ratios
  Answer: b
45. The y-intercept of a line y = 3x + 4 is:
  a) 3
  b) 4
  c) -3
  d) 0
  Answer: b
46. The distance formula is based on:
  a) Midpoint Theorem
  b) Pythagoras Theorem
  c) Section Formula
  d) Centroid Theorem
  Answer: b
47. The slope of the line x = 3 is:
  a) 3
  b) 1
  c) 0
  d) Undefined
  Answer: d
48. The coordinates of the midpoint of the segment joining (2, 3) and (4, 5) are:
  a) (3, 4)
  b) (2, 4)
  c) (3, 5)
  d) (2, 3)
  Answer: a
49. A triangle with vertices (0, 0), (6, 0), and (0, 8) is:
  a) Isosceles
  b) Right-angled
  c) Equilateral
  d) Both a and b
  Answer: d
50. A quadrilateral is a rhombus if:
  a) All sides are equal
  b) Opposite angles are equal
  c) Diagonals bisect each other at right angles
  d) All of the above
  Answer: d