Class 9 Maths Coordinate Geometry MCQs with Answer

Class 9 Maths Coordinate Geometry MCQs

Coordinate Geometry is one of the most interesting chapters in Class 9 Maths because it connects numbers with geometry in a visual and practical way. This section on Class 9 Maths Coordinate Geometry MCQs with Answer is designed to help students understand concepts easily through important multiple-choice questions based on the latest CBSE syllabus.

The coordinate geometry class 9 mcq set includes questions on Cartesian plane, coordinate axes, origin, quadrants, plotting points, and identifying coordinates on a graph. Students can also practice class 9 maths chapter 3 mcq with answers to improve conceptual clarity and strengthen problem-solving skills step by step. Regular practice of coordinate geometry mcq class 9 helps students avoid confusion while plotting points and improves accuracy in exams.

In addition, students can attempt a class 9 maths chapter 3 mcq online test to improve speed and confidence. These MCQs are based on important concepts like x-axis, y-axis, ordered pairs, signs of coordinates in different quadrants, and representation of points on the Cartesian plane. Sometimes students understand the theory but make mistakes while identifying coordinates or quadrants. That is why consistent practice is very important for scoring better marks.

What is Coordinate Geometry MCQ Class 9?

Coordinate Geometry MCQs for Class 9 Maths are multiple-choice questions that test a student’s understanding of graphs, coordinates, and plotting points on the Cartesian plane. These questions are an important part of Class 9 Maths Chapter 3 MCQs with answers and help students prepare effectively for exams.

In these questions, students learn about coordinate axes, origin, quadrants, ordered pairs, and the position of points on a graph. They also practice identifying coordinates correctly and understanding the relation between geometry and algebra.

Regular practice of coordinate geometry mcq class 9 improves visualization skills, accuracy, and confidence. It also helps students perform better in CBSE Board exams and online tests.

Important Terms in Coordinate Geometry

This table is very useful for solving class 9 maths chapter 3 mcq online test questions quickly and accurately.

Important Tricks for Coordinate Geometry MCQs (Class 9)

Here are some simple tricks used in coordinate geometry class 9 mcq questions:

Remember the Sign Rule:
First Quadrant = (+, +)
Second Quadrant = (-, +)
Third Quadrant = (-, -)
Fourth Quadrant = (+, -)

Always Read Ordered Pairs Carefully:
The first value represents x-coordinate and the second value represents y-coordinate.

Origin Point:
The coordinates of origin are always (0, 0).

Axes Identification:
If y-coordinate is 0, the point lies on x-axis.
If x-coordinate is 0, the point lies on y-axis.

These tricks are very helpful in solving class 9 maths coordinate geometry MCQs with answers.

Q. Which of the following statements best describes the primary connection between geometry and algebra in Coordinate Geometry?

1. Coordinate Geometry uses geometric shapes to solve algebraic equations.
2. Coordinate Geometry represents geometric figures and their properties using algebraic equations and coordinates.
3. Coordinate Geometry is a branch of algebra that focuses on geometric proofs.
4. Coordinate Geometry solely deals with plotting points without any algebraic interpretation.

Answer: B

Explanation:

Coordinate Geometry, also known as Analytical Geometry, provides a way to describe geometric objects using numerical coordinates and algebraic equations. This allows for the study of geometry using algebraic methods, and vice versa.

Q. In the Cartesian plane, what are the two perpendicular lines used to locate points called?

1. Axes of symmetry
2. Coordinate axes
3. Reference lines
4. Geometric lines

Answer: B

Explanation:

The Cartesian plane is defined by two perpendicular number lines, usually called the x-axis (horizontal) and the y-axis (vertical), which intersect at the origin. These are collectively known as the coordinate axes.

Q. What is the significance of the 'origin' in the Cartesian coordinate system?

1. It is the point where the x-axis and y-axis intersect, representing the (0,0) coordinate.
2. It is the starting point for all positive coordinates.
3. It defines the slope of the x-axis.
4. It is the center of the first quadrant.

Answer: A

Explanation:

The origin (0,0) is the unique point where the x-axis and y-axis cross. All other points in the Cartesian plane are located with respect to this origin using ordered pairs.

Q. A point is located at (-3, 5) in the Cartesian plane. In which quadrant does this point lie?

1. Quadrant I
2. Quadrant II
3. Quadrant III
4. Quadrant IV

Answer: B

Explanation:

In Quadrant I, both x and y coordinates are positive (+,+). In Quadrant II, x is negative and y is positive (-,+). In Quadrant III, both x and y are negative (-,-). In Quadrant IV, x is positive and y is negative (+,-). Since -3 is negative and 5 is positive, the point (-3, 5) is in Quadrant II.

Q. If a point has coordinates (x, 0), where would it be located on the Cartesian plane?

1. On the y-axis
2. On the x-axis
3. In Quadrant I or IV
4. At the origin

Answer: B

Explanation:

Any point with a y-coordinate of 0 lies on the x-axis. Similarly, any point with an x-coordinate of 0 lies on the y-axis. The origin (0,0) is the only point that lies on both axes.

Q. Consider a point P with coordinates (a, b). If point Q is the reflection of P across the y-axis, what are the coordinates of Q?

1. (a, -b)
2. (-a, b)
3. (-a, -b)
4. (b, a)

Answer: B

Explanation:

When a point is reflected across the y-axis, its x-coordinate changes sign while its y-coordinate remains the same. So, (a, b) becomes (-a, b).

Q. Which of the following real-life applications heavily relies on Coordinate Geometry for its functionality?

1. Calculating the volume of a liquid
2. Predicting weather patterns
3. GPS navigation systems
4. Determining the chemical composition of a substance

Answer: C

Explanation:

GPS (Global Positioning System) navigation systems use a network of satellites to determine precise geographical coordinates (latitude and longitude) of a receiver, which is a direct application of coordinate geometry to represent locations and distances.

Q. What is the distance of the point (4, -3) from the x-axis?

1. 4 units
2. 3 units
3. 5 units
4. -3 units

Answer: B

Explanation:

The distance of a point (x, y) from the x-axis is given by the absolute value of its y-coordinate, |y|. In this case, the y-coordinate is -3, so the distance is |-3| = 3 units.

Q. The ordered pair (x, y) represents a point in the Cartesian plane. What does 'x' specifically denote?

1. The vertical distance from the origin
2. The abscissa or the horizontal distance from the y-axis
3. The ordinate or the vertical distance from the x-axis
4. The angle of the point from the x-axis

Answer: B

Explanation:

In an ordered pair (x, y), 'x' is called the abscissa, representing the horizontal displacement from the y-axis. 'y' is called the ordinate, representing the vertical displacement from the x-axis.

Q. Which quadrant contains points where the product of the x and y coordinates is always positive?

1. Quadrant I only
2. Quadrant II only
3. Quadrant I and Quadrant III
4. Quadrant II and Quadrant IV

Answer: C

Explanation:

In Quadrant I, both x and y are positive, so x * y > 0. In Quadrant III, both x and y are negative, so x * y = (-x) * (-y) = xy > 0. In Quadrant II and IV, one coordinate is positive and the other is negative, resulting in a negative product.

Q. A point P(x, y) is equidistant from the points A(0, 0) and B(2, 0). Which of the following equations must be true for point P?

x = 1

y = 1

x + y = 2

x2 + y2 = 4

Answer: A

Explanation:

If P(x, y) is equidistant from A(0, 0) and B(2, 0), then PA² = PB². Using the distance formula: (x-0)² + (y-0)² = (x-2)² + (y-0)². This simplifies to x² + y² = x² - 4x + 4 + y². Further simplification gives 0 = -4x + 4, which means 4x = 4, so x = 1. This means P lies on the perpendicular bisector of the line segment AB, which is the line x=1.

Q. The vertices of a triangle are A(0, 6), B(8, 0), and C(0, 0). What type of triangle is ABC?

1. Equilateral triangle
2. Isosceles triangle
3. Scalene triangle
4. Right-angled triangle

Answer: D

Explanation:

Calculate the lengths of the sides using the distance formula: AB = √((8-0)² + (0-6)²) = √(64 + 36) = √100 = 10 units. BC = √((0-8)² + (0-0)²) = √(64 + 0) = √64 = 8 units. CA = √((0-0)² + (6-0)²) = √(0 + 36) = √36 = 6 units. Check for Pythagorean theorem: CA² + BC² = 6² + 8² = 36 + 64 = 100. And AB² = 10² = 100. Since CA² + BC² = AB², the triangle is a right-angled triangle, with the right angle at C(0,0).

Q. The coordinates of the midpoint of a line segment joining P(x1, y1) and Q(x2, y2) are given by:

1. ((x1 - x2)/2, (y1 - y2)/2)
2. ((x1 + x2)/2, (y1 + y2)/2)
3. (x1 + x2, y1 + y2)
4. (√((x2 - x1)²) , √((y2 - y1)²))

Answer: B

Explanation:

The midpoint formula is used to find the coordinates of the point that is exactly halfway between two given points. It averages the x-coordinates and the y-coordinates separately.

Q. What is the area of the triangle with vertices (0, 0), (5, 0), and (0, 7)?

1. 12.5 square units
2. 17.5 square units
3. 35 square units
4. 70 square units

Answer: B

Explanation:

The vertices (0, 0), (5, 0), and (0, 7) form a right-angled triangle with the right angle at the origin. The base can be considered as the distance between (0,0) and (5,0), which is 5 units. The height can be considered as the distance between (0,0) and (0,7), which is 7 units. The area of a triangle = (1/2) * base * height = (1/2) * 5 * 7 = 35/2 = 17.5 square units.

Q. A line segment has endpoints A(2, 3) and B(8, 11). What are the coordinates of the point that divides the segment AB in the ratio 1:3 internally?

1. (3.5, 5)
2. (4, 6)
3. (5, 7)
4. (6.5, 9)

Answer: C

Explanation:

Using the section formula for internal division: P(x, y) = ((m x₂ + n x₁)/(m + n), (m y₂ + n y₁)/(m + n)). Here, (x₁, y₁) = (2, 3), (x₂, y₂) = (8, 11), and m:n = 1:3. x = (1*8 + 3*2)/(1+3) = (8+6)/4 = 14/4 = 3.5 y = (1*11 + 3*3)/(1+3) = (11+9)/4 = 20/4 = 5 So, the coordinates are (3.5, 5).

Q. If the distance between the points (k, 2) and (4, 3) is √10, what is the value of k?

1. 1 or 7
2. 2 or 6
3. 3 or 5
4. 0 or 8

Answer: A

Explanation: 

Using the distance formula: D = √((x₂ - x₁)² + (y₂ - y₁)²). √10 = √((4 - k)² + (3 - 2)²) Square both sides: 10 = (4 - k)² + (1)² 10 = (4 - k)² + 1 9 = (4 - k)² Taking the square root of both sides: ±3 = 4 - k Case 1: 3 = 4 - k ⇒ k = 4 - 3 ⇒ k = 1 Case 2: -3 = 4 - k ⇒ k = 4 + 3 ⇒ k = 7 So, k can be 1 or 7.

Q. The coordinates of the centroid of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) are given by:

1. ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)
2. ((x1 + x2)/2, (y1 + y2)/2)
3. (x1 + x2 + x3, y1 + y2 + y3)
4. ((x1 - x2 - x3)/3, (y1 - y2 - y3)/3)

Answer: A

Explanation:

The centroid of a triangle is the point of intersection of its medians. Its coordinates are found by averaging the x-coordinates and the y-coordinates of the three vertices.

Q. What is the slope of the line passing through the points (2, 5) and (6, 13)?

1. 1/2
2. 2
3. -2
4. 4

Answer: B

Explanation:

The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula m = (y₂ - y₁)/(x₂ - x₁). Here, (x₁, y₁) = (2, 5) and (x₂, y₂) = (6, 13). m = (13 - 5)/(6 - 2) = 8/4 = 2.

Q. If the points A(1, 2), B(4, y), C(x, 6), and D(3, 5) are the vertices of a parallelogram taken in order, then what are the values of x and y?

1. x = 6, y = 3
2. x = 3, y = 6
3. x = 5, y = 2
4. x = 2, y = 5

Answer: A

Explanation:

In a parallelogram, the diagonals bisect each other. This means the midpoint of AC is the same as the midpoint of BD. Midpoint of AC: ((1+x)/2, (2+6)/2) = ((1+x)/2, 4) Midpoint of BD: ((4+3)/2, (y+5)/2) = (7/2, (y+5)/2) Equating the x-coordinates: (1+x)/2 = 7/2 ⇒ 1+x = 7 ⇒ x = 6. Equating the y-coordinates: 4 = (y+5)/2 ⇒ 8 = y+5 ⇒ y = 3. So, x = 6 and y = 3.

Q. A circle has its center at the origin (0,0) and passes through the point (3, 4). What is the radius of the circle?

1. 3 units
2. 4 units
3. 5 units
4. 7 units

Answer: C

Explanation:

The radius of the circle is the distance between its center (0,0) and any point on its circumference (3,4). Using the distance formula: r = √((3-0)² + (4-0)²) = √(3² + 4²) = √(9 + 16) = √25 = 5 units.

Q. The equation of a straight line passing through the origin (0,0) and the point (3, 6) is:

1. y = x + 3
2. y = 2x
3. y = x/2
4. y - x = 0

Answer: B

Explanation:

First, find the slope (m) of the line using the two points (0,0) and (3,6): m = (6 - 0)/(3 - 0) = 6/3 = 2. Since the line passes through the origin, its y-intercept is 0. Using the slope-intercept form (y = mx + c), where c is the y-intercept: y = 2x + 0 y = 2x.

Q. What is the condition for two lines with slopes m1 and m2 to be perpendicular?

1. m1 = m2
2. m1 + m2 = 0
3. m1 * m2 = -1
4. m1 / m2 = 1

Answer: C

Explanation:

For two non-vertical lines to be perpendicular, the product of their slopes must be -1. If one line is vertical (undefined slope), the other must be horizontal (slope 0).

Q. The coordinates of the vertices of a square are (0, 0), (a, 0), (a, a), and (0, a). What is the length of its diagonal?

1. a
2. 2a
3. a√2
4. A√3

Answer: C

Explanation:

The diagonal connects opposite vertices, for example, (0,0) and (a,a). Using the distance formula: Diagonal length = √((a-0)² + (a-0)²) = √(a² + a²) = √(2a²) = a√2 units.

Q. A point (x, y) is on the line y = 3x - 1. If its x-coordinate is 2, what is its y-coordinate?

1. 2
2. 3
3. 5
4. 7

Answer: C

Explanation:

Substitute x = 2 into the equation y = 3x - 1: y = 3(2) - 1 y = 6 - 1 y = 5.

Q. The coordinates of the vertices of a parallelogram are (1, 2), (4, 2), (3, 5), and (x, y). What are the coordinates (x, y) of the fourth vertex?

1. (0, 5)
2. (6, 5)
3. (0, 3)
4. (2, 3)

Answer: A

Explanation:

Let the vertices be A(1, 2), B(4, 2), C(3, 5), and D(x, y). In a parallelogram, the diagonals bisect each other. So the midpoint of AC is the same as the midpoint of BD. Midpoint of AC = ((1+3)/2, (2+5)/2) = (4/2, 7/2) = (2, 3.5) Midpoint of BD = ((4+x)/2, (2+y)/2) Equating the coordinates: (4+x)/2 = 2 ⇒ 4+x = 4 ⇒ x = 0 (2+y)/2 = 3.5 ⇒ 2+y = 7 ⇒ y = 5 So, the fourth vertex is (0, 5).

Q. What is the equation of the line that is parallel to the x-axis and passes through the point (5, -2)?

1. x = 5
2. y = -2
3. y = x - 7
4. x + y = 3

Answer: B

Explanation:

A line parallel to the x-axis has a constant y-coordinate. Since it passes through (5, -2), its y-coordinate must always be -2. Thus, the equation is y = -2.

Q. If the distance of a point P(x, y) from the origin is 5 units, which of the following equations represents the locus of P?

1. x + y = 5
2. x² + y² = 5
3. x² + y² = 25
4. x = 5, y = 5

Answer: C

Explanation:

The distance of a point (x, y) from the origin (0, 0) is given by √((x-0)² + (y-0)²) = √(x² + y²). If this distance is 5, then √(x² + y²) = 5. Squaring both sides gives x² + y² = 25. This is the equation of a circle centered at the origin with a radius of 5.

Q. The x-intercept of the line 3x + 4y = 12 is:

1. 3
2. 4
3. -3
4. -4

Answer: B

Explanation:

To find the x-intercept, set y = 0 in the equation of the line: 3x + 4(0) = 12 3x = 12 x = 12/3 x = 4. So, the x-intercept is 4.

Q. Which of the following points lies on the line segment connecting (1, 1) and (5, 5)?

1. (0, 0)
2. (3, 3)
3. (6, 6)
4. (2, 4)

Answer: B

Explanation:

The line segment connecting (1, 1) and (5, 5) is part of the line y = x. For a point (x,y) to be on the segment, it must satisfy y=x and its x-coordinate must be between 1 and 5 (inclusive), and similarly for y-coordinate. (0,0) satisfies y=x but 0 is not between 1 and 5. (3,3) satisfies y=x and 3 is between 1 and 5. (6,6) satisfies y=x but 6 is not between 1 and 5. (2,4) does not satisfy y=x.

Q. If the points (a, 0), (0, b) and (1, 1) are collinear, then which of the following relations is true?

1. a + b = ab
2. a - b = ab
3. ab = 1
4. a + b = 1

Answer: A

Explanation:

For three points to be collinear, the slope between the first two points must be equal to the slope between the second two points. Slope between (a, 0) and (0, b): m₁ = (b - 0)/(0 - a) = b/(-a) = -b/a Slope between (0, b) and (1, 1): m₂ = (1 - b)/(1 - 0) = 1 - b Equating the slopes: -b/a = 1 - b -b = a(1 - b) -b = a - ab ab = a + b.

Coordinate Geometry MCQ Preparation Tips

Follow these simple tips to score better:

Practice plotting points regularly on graph paper

Learn quadrant signs carefully to avoid confusion

Read ordered pairs in the correct sequence

Revise coordinate rules before attempting MCQs

Solve coordinate geometry mcq class 9 online tests for better practice

Use NCERT and CBSE-based study material for preparation

Conclusion

Practicing Class 9 Maths Coordinate Geometry MCQs with answers is one of the best ways to improve graph understanding and visualization skills. It helps students build a strong foundation for higher mathematics and improves confidence in solving coordinate-based problems.

Regular practice also helps students reduce mistakes while identifying coordinates, plotting points, and understanding quadrants in exams and online tests.