Coordinate Geometry is one of the most important chapters in Class 9 Maths. It forms the foundation for higher classes and competitive exams. In this post, we have compiled the Top 50 MCQs based on basic concepts, distance formula, midpoint formula, and higher-order thinking questions. These questions will help students revise quickly and improve accuracy.
TOP 50 MCQs – COORDINATE GEOMETRY (CLASS 9)
- The x-coordinate is also called:
A) Ordinate
B) Abscissa
C) Origin
D) Axis - Point (3, -4) lies in:
A) I Quadrant
B) II Quadrant
C) III Quadrant
D) IV Quadrant - Distance of point (-3,-4) from origin:
A) 5
B) 6
C) 7
D) 4 - Distance between (-1,2) and (3,2):
A) 4
B) 5
C) 6
D) 7 - Midpoint of (-2,2) and (2,6):
A) (0,4)
B) (1,4)
C) (0,2)
D) (2,4) - Find centre if endpoints of diameter are (2,2) and (6,6).
A) (4,4)
B) (3,3)
C) (5,5)
D) (2,4) - If midpoint is (3,3) and one point is (1,1), find other point:
A) (5,5)
B) (4,4)
C) (3,5)
D) (2,2) - Midpoint of (a,b) and (-a,-b):
A) (0,0)
B) (a,b)
C) (-a,-b)
D) (1,1) - If a point lies on y-axis, its x-coordinate is: A) 1
B) 0
C) −1
D) Any number - If midpoint is (0,0), endpoints are: A) Same sign
B) Opposite sign
C) Both positive
D) Both negative - The point whose ordinate is 4 and which lies on y-axis is:
A) (4, 0)
B) (0, 4)
C) (1, 4)
D) (4, 2) - Which of the points P(0, 3), Q(1, 0), R(0, −1), S(−5, 0), T(1, 2) do not lie on the x-axis?
A) P AND R ONLY
B) Q AND S ONLY
C) P, R AND T
D) Q, S AND T - The point which lies on y-axis at a distance of 5 units in the negative direction of y-axis is:
A) (0, 5)
B) (5, 0)
C) (0, −5)
D) (−5, 0) - If the co-ordinates of a point are (−5, 6), the perpendicular distance of the point from y-axis is:
A) 5 UNITS
B) 6 UNITS
C) 7 UNITS
D) 7.5 UNITS - If the distance between the points (2, −2) and (−1, x) is 5, one of the value of x is:
A) −2
B) 2
C) −1
D) 1 - AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is:
A) 5
B) 3
C) √34
D) 4 - The points (−4, 0), (4, 0) and (0, 3) are the vertices of a:
A) Right triangle
B) Isosceles triangle
C) Equilateral triangle
D) Scalene triangle - The point which lies on the perpendicular bisector of the line segment joining the points A(−2, −5) and B(2, 5) is:
A) (0, 0)
B) (0, 2)
C) (2, 0)
D) (−2, 0) - The fourth vertex D of a parallelogram ABCD whose three vertices are A(−2, 3), B(6, 7) and C(8, 3) is:
A) (0, 1)
B) (0, −1)
C) (−1, 0)
D) (1, 0) - The points A(9, 0), B(9, 6), C(−9, 6) and D(−9, 0) are the vertices of a:
A) Square
B) Rectangle
C) Rhombus
D) Trapezium - The sum of the distances of point (a, b) from the coordinate axes is:
A) a + b
B) |a| + b
C) |b| + a
D) |a| + |b| - The perimeter of the triangle formed by the points (0, 0), (1, 0) and (0, 1) is:
A) 1 ± √2
B) √2 + 1
C) 3
D) 2 + √2 - A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is:
A) 9, 6
B) 3, −9
C) −3, 9
D) 9, −6 - Calculate the value of x such that the points A(x,2), B(-3,-4), and C(7,-5) lie on a straight line.
A. -63
B. 63
C. 60
D. -60 - Find the ratio in which the y-axis divides the line segment connecting the points (-3,-4) and (1,-2).
A. 1:3
B. 2:3
C. 3:1
D. 2:3 - Which point on the x-axis is at an equal distance from the points (-1, 0) and (5, 0)?
A. (0, 2)
B. (2, 0)
C. (3, 0)
D. (0, 3) - If A(5, 3), B(11, -5), and P(12, y) are the vertices of a right-angled triangle with the right angle at P, what is y?
A. -2, 4
B. -2, -4
C. 2, -4
D. 2, 4 - If the points P(2,4), Q(0,3), R(3,6), and S(5,y) represent the vertices of a parallelogram PQRS, find the value of y.
A. 7
B. 5
C. -7
D. -8 - What is the total perimeter of a triangle having vertices at (0, 4), (0, 0), and (3, 0)?
A. 7
B. 5
C. 10
D. 12 - Given that A(5, p), B(1, 5), C(2, 1), and D(6, 2) form the square ABCD, find the value of p.
A. 7
B. 3
C. 6
D. 8 - Identify the coordinates of the circumcentre for a triangle with vertices O(0, 0), A(a, 0), and B(0, b).
A. (a, b)
B. (a/2, b/2)
C. (b/2, a/2)
D. (b, a) - Find the point on the x-axis that lies on the perpendicular bisector of the segment joining (7, 6) and (-3, 4).
A. (0, 2)
B. (3, 0)
C. (0, 3)
D. (2, 0) - The length of the segment joining A(2, -3) and B is 10 units. If the x-coordinate of B is 10, what could the y-coordinate be?
A. 3 or -9
B. -3 or 9
C. 6 or 27
D. -6 or -27 - If point (x, y) is 5 units from the origin, how many such points can exist in the third quadrant?
A. 0
B. 1
C. 2
D. infinitely many - If the distance between (3, -5) and (x, -5) is exactly 15 units, what are the possible values of x?
A. 12, -18
B. -12, 18
C. 18, 5
D. -9, -12 - XOYZ is a rectangle with vertices at X(-3, 0), O(0, 0), and Y(0, 4). Calculate the length of its diagonal.
A. 5 units
B. √5 units
C. x² + y² units
D. 4 units - If the origin is the midpoint of the segment connecting P(a, b) and Q(3, 3), what is the value of (a + b)?
A. 0
B. 3
C. 6
D. -6 - On which axis does the midpoint of the line segment joining P(-4, 5) and Q(4, 6) lie?
A. x-axis
B. y-axis
C. origin
D. neither x-axis nor y-axis - What type of triangle is formed by the vertices (-5, 0), (5, 0), and (0, 4)?
A. right-angled triangle
B. isosceles triangle
C. equilateral triangle
D. scalene triangle - Find the perimeter of the triangle created by the points (0, 0), (2, 0), and (0, 2).
A. 4 units
B. 6 units
C. 6√2 units
D. 4 + 2√2 units - A line x/4 + y/6 = 1 intersects the axes at P and Q. Find the midpoint of segment PQ.
A. (2, 3)
B. (3, 2)
C. (2, 0)
D. (0, 3) - If (2, 6) is the midpoint of the line segment joining (a, 4) and (2, 2b), calculate the value of a + b.
A. 6
B. 7
C. 8
D. 16 - AOBC is a rectangle with vertices A(0, 2), O(0, 0), and B(4, 0). What is the square of the length of its diagonal?
A. 36
B. 20
C. 16
D. 4 - If the mirror image of the point P(5, 2) in the x-axis is Q and the image of Q in the y-axis is R, what are the coordinates of R?
A) (5, –2)
B) (–5, –2)
C) (–5, 2)
D) (2, 5) - In which quadrants are the signs of both coordinates the same?
A) I AND II
B) II AND III
C) I AND III
D) II AND IV - What is the equation of the x-axis?
A) x = 0
B) y = 0
C) x = a
D) y = a - What is the equation of a line parallel to the x-axis?
A) x = 0
B) y = 0
C) x = a
D) y = a - What is the equation of a line parallel to the y-axis?
A) x = 0
B) y = 0
C) x = a
D) y = a - Any point on the x-axis is of the form:
A) (x, 0)
B) (0, y)
C) (x, y)
D) (y, x) - If x > 0 and y < 0, then the point (x, y) lies in which quadrant?
A) I
B) II
C) III
D) IV
ANSWER KEY
1B 2D 3A 4A 5A 6A 7A 8A 9B 10B
11B 12C 13C 14A 15A 16C 17B 18A 19A 20B 21D 22D 23A 24A 25A 26B 27B 28D 29D 30D 31D 32A 33B 34B 35D 36D 37A 38A 39D 40B 41B 42B 43C 44B 45D 46A 47D 48C 49A 50D
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