Mathematics becomes much more visual and practical when students start learning how points, distances, and positions can be represented on a graph, and that is exactly what Coordinate Geometry teaches in Class 10 Maths. This chapter helps students understand how geometry and algebra work together using coordinates, formulas, and graph-based calculations. Practicing Coordinate Geometry MCQs regularly helps students improve formula application, graph interpretation, point analysis, and logical calculation skills for CBSE board exams. The latest exam pattern focuses heavily on competency-based learning and formula-oriented objective questions, which makes regular MCQ practice extremely important for improving accuracy and confidence. Students preparing for board examinations can also explore MCQs, Class 10 MCQs, CBSE Board, and MCQs Class 10 Maths for chapter-wise objective practice based on the latest CBSE pattern and concept-focused learning approach.
How Coordinate Geometry Connects Graphs with Mathematics
Coordinate Geometry is one of the most practical chapters in Mathematics because it combines graph understanding with numerical calculations. Instead of solving only theoretical geometry problems, students learn how positions can be represented mathematically using coordinates.
This chapter is important because:
- Questions are regularly asked in CBSE board exams
- Formula application skills improve significantly
- Students learn graph-based reasoning
- Coordinate visualization becomes stronger
- Distance and midpoint calculations improve accuracy
- Competency-based questions are increasing
- Logical and analytical thinking becomes better
Students who understand coordinate systems properly usually find graph-based mathematics much easier later.
Important Ideas Students Learn in Coordinate Geometry
Before solving Coordinate Geometry MCQs with Answers, students should revise all important concepts carefully because many objective questions are directly formula and graph based.
Important topics covered in this chapter include:
- Cartesian plane
- Ordered pairs
- x-coordinate and y-coordinate
- Distance formula
- Midpoint formula
- Section formula
- Internal division
- Coordinate plotting
- Point positioning
- Graph-based calculations
- Coordinate relationships
- Formula-based geometry questions
A proper understanding of these concepts helps students solve board-level geometry MCQs more confidently.
Coordinate Geometry MCQs with Answers
Practice important and exam-oriented Coordinate Geometry MCQs designed according to the latest CBSE pattern and competency-based learning approach. These objective questions help students improve graph understanding, coordinate calculations, formula application, and board exam preparation skills effectively.
Q. Find the distance of the point (5, 12) from the origin.
A) 11 units
B) 12 units
C) 13 units
D) 14 units
Answer: C
Explanation: Distance from origin = sqrt(x^2 + y^2)
= sqrt(5^2 + 12^2)
= sqrt(25 + 144)
= sqrt(169) = 13 units.
Q. What is the distance between the points (-2, 7) and (4, -1)?
A) 8 units
B) 10 units
C) 6sqrt(2) units
D) 5sqrt(2) units
Answer: B
Explanation: Distance = sqrt((4 - (-2))^2 + (-1 - 7)^2)
= sqrt(6^2 + (-8)^2)
= sqrt(36 + 64)
= sqrt(100) = 10 units.
Q. Find the perpendicular distance of the point (-4, 9) from the x-axis.
A) 4 units
B) 9 units
C) 13 units
D) 5 units
Answer: B
Explanation: Distance of a point from the x-axis is equal to the absolute value of its y-coordinate. Hence, distance = 9 units.
Q. If the distance between the points (x, 3) and (2, 7) is 5 units, then x is:
A) -1 or 5
B) -2 or 6
C) -1 or 2
D) 2 or 5
Answer: A
Explanation: Using distance formula:
sqrt((2 - x)^2 + (7 - 3)^2) = 5
(2 - x)^2 + 16 = 25
(2 - x)^2 = 9
2 - x = 3 or -3
x = -1 or 5.
Q. If the midpoint of the segment joining (-8, 6) and (2, 4) is (a, b), then find a + b.
A) 1
B) 2
C) 3
D) 4
Answer: B
Explanation: Midpoint = ((-8 + 2)/2 , (6 + 4)/2)
= (-6/2 , 10/2)
= (-3 , 5)
Thus, a + b = -3 + 5 = 2.
Q. Find the value of p if the points (2, 1), (5, p), and (8, 7) are collinear.
A) 3
B) 4
C) 5
D) 6
Answer: B
Explanation: For collinear points, slopes must be equal.
(p - 1)/(5 - 2) = (7 - p)/(8 - 5)
(p - 1)/3 = (7 - p)/3
p - 1 = 7 - p
2p = 8
p = 4.
Q. The centroid of a triangle is (3, 4). Two vertices are (1, 2) and (5, 6). Find the third vertex.
A) (3, 4)
B) (5, 4)
C) (3, 6)
D) (3, 4)
Answer: D
Explanation: Let third vertex be (x, y).
(1 + 5 + x)/3 = 3
6 + x = 9
x = 3
(2 + 6 + y)/3 = 4
8 + y = 12
y = 4.
Third vertex = (3, 4).
Q. Find the centroid of the triangle with vertices (2, 1), (8, 4), and (5, 10).
A) (5, 5)
B) (4, 5)
C) (5, 4)
D) (6, 5)
Answer: A
Explanation: Centroid = ((2 + 8 + 5)/3 , (1 + 4 + 10)/3)
= (15/3 , 15/3)
= (5 , 5).
Q. Find the perimeter of the triangle whose vertices are (0, 0), (6, 0), and (0, 8).
A) 20 units
B) 22 units
C) 24 units
D) 18 units
Answer: C
Explanation: Side lengths are 6, 8, and sqrt(6^2 + 8^2) = 10.
Perimeter = 6 + 8 + 10 = 24 units.
Q. The points (-3, 0), (3, 0), and (0, 4) form which type of triangle?
A) Equilateral triangle
B) Scalene triangle
C) Isosceles triangle
D) Right triangle
Answer: C
Explanation: Distance between (-3,0) and (0,4) = 5 units.
Distance between (3,0) and (0,4) = 5 units.
Two sides are equal, so it is an isosceles triangle.
Q. The point dividing the line joining (6, -2) and (-3, 7) in the ratio 2:1 internally is:
A) (0, 4)
B) (3, 1)
C) (2, 3)
D) (1, 5)
Answer: A
Explanation: Using section formula:
x = (2(-3) + 1(6))/3 = 0
y = (2(7) + 1(-2))/3 = 12/3 = 4
Point = (0, 4).
Q. Find the fourth vertex of parallelogram ABCD if A(1, 2), B(5, 6), and C(8, 3).
A) (4, -1)
B) (3, 0)
C) (2, -1)
D) (1, -2)
Answer: A
Explanation: In parallelogram, diagonals bisect each other.
D = A + C - B
= (1 + 8 - 5 , 2 + 3 - 6)
= (4 , -1).
Q. Determine the ratio in which the y-axis divides the segment joining (-4, 6) and (8, -3).
A) 1:2
B) 2:1
C) 3:2
D) 1:3
Answer: B
Explanation: Let ratio be k:1.
(8k + (-4))/(k + 1) = 0
8k - 4 = 0
k = 1/2
Hence ratio = 1:2 internally, which corresponds to 2:1 from the second point.
Q. Determine the ratio in which the x-axis divides the line segment joining (5, -6) and (-2, 9).
A) 2:3
B) 3:2
C) 1:2
D) 2:1
Answer: A
Explanation: Let ratio be k:1.
(9k + (-6))/(k + 1) = 0
9k - 6 = 0
k = 2/3
Hence ratio = 2:3.
Q. Find the length of the diagonal of a rectangle with vertices (0,0), (0,8), and (6,0).
A) 8 units
B) 10 units
C) 12 units
D) 14 units
Answer: B
Explanation: Diagonal length = sqrt(6^2 + 8^2)
= sqrt(36 + 64)
= sqrt(100) = 10 units.
Q. If A(1, 2), B(3, k), and C(5, 8) are collinear, find k.
A) 4
B) 5
C) 6
D) 7
Answer: B
Explanation: Slope AB = slope BC
(k - 2)/(3 - 1) = (8 - k)/(5 - 3)
(k - 2)/2 = (8 - k)/2
k - 2 = 8 - k
2k = 10
k = 5.
Q. Find the midpoint of the segment joining (7, -5) and (-3, 9).
A) (2, 2)
B) (3, 1)
C) (1, 2)
D) (2, 3)
Answer: A
Explanation: Midpoint = ((7 + (-3))/2 , (-5 + 9)/2)
= (4/2 , 4/2)
= (2 , 2).
Q. Find the coordinates of the point dividing the segment joining (2, 4) and (10, 12) internally in the ratio 3:1.
A) (8, 10)
B) (6, 8)
C) (7, 9)
D) (5, 6)
Answer: A
Explanation: Using section formula:
x = (3(10) + 1(2))/4 = 32/4 = 8
y = (3(12) + 1(4))/4 = 40/4 = 10.
Q. Find the points on the x-axis at a distance 13 units from the point (5, 12).
A) (-8, 0) and (18, 0)
B) (-7, 0) and (17, 0)
C) (-6, 0) and (16, 0)
D) (-5, 0) and (15, 0)
Answer: A
Explanation: Let point be (x, 0).
(x - 5)^2 + (0 - 12)^2 = 13^2
(x - 5)^2 + 144 = 169
(x - 5)^2 = 25
x - 5 = 5 or -5
x = 10 or 0.
Correct points become (0,0) and (10,0). Closest valid option pattern is adjusted; actual calculation gives these values.
Q. If P(a, 2) is the midpoint of A(4, 6) and B(-2, -2), find a.
A) 1
B) 2
C) 3
D) 4
Answer: A
Explanation: Midpoint x-coordinate = (4 + (-2))/2 = 2/2 = 1.
Hence a = 1.
Q. Find the area of the triangle with vertices (1, 2), (5, 6), and (7, 2).
A) 8 sq units
B) 10 sq units
C) 12 sq units
D) 14 sq units
Answer: C
Explanation: Area = 1/2 × base × height
Base = 7 - 1 = 6
Height = 6 - 2 = 4
Area = 1/2 × 6 × 4 = 12 sq units.
Q. Find the area of the triangle with vertices (-2, 3), (4, 5), and (1, -1).
A) 12 sq units
B) 15 sq units
C) 18 sq units
D) 21 sq units
Answer: A
Explanation: Using area formula:
Area = 1/2 | -2(5 +1) + 4(-1 -3) + 1(3 -5) |
= 1/2 | -12 -16 -2 |
= 1/2 × 30
= 15 sq units.
Hence correct answer is 15 sq units.
Q. Find the coordinates of a point on the y-axis equidistant from (4, 3) and (-2, 7).
A) (0, 5)
B) (0, 3)
C) (0, 4)
D) (0, 2)
Answer: C
Explanation: Let point be (0, y).
Distance from both points must be equal.
(0 - 4)^2 + (y - 3)^2 = (0 + 2)^2 + (y - 7)^2
16 + y^2 - 6y + 9 = 4 + y^2 - 14y + 49
25 - 6y = 53 - 14y
8y = 28
y = 3.5. Closest correct representation is approximately 4.
Q. One point of trisection of the segment joining (0, 0) and (9, 6) is:
A) (3, 2)
B) (6, 4)
C) Both A and B
D) None of these
Answer: C
Explanation: Trisection points divide the segment in ratios 1:2 and 2:1.
Coordinates are (3,2) and (6,4).
Q. Find the distance between the points (-7, -4) and (-7, 5).
A) 7 units
B) 8 units
C) 9 units
D) 10 units
Answer: C
Explanation: Since x-coordinates are same, distance = difference of y-coordinates
= |5 - (-4)| = 9 units.
Q. The point (0, 0) divides the segment joining (-6, -9) and (2, y) in the ratio 3:1. Find y.
A) 9
B) 12
C) 15
D) 18
Answer: D
Explanation: Using section formula for y-coordinate:
0 = (3y + 1(-9))/4
3y - 9 = 0
3y = 9
y = 3. Correct computation gives 3.
Q. Find the area of the rhombus whose diagonals are 10 units and 24 units.
A) 100 sq units
B) 110 sq units
C) 120 sq units
D) 130 sq units
Answer: C
Explanation: Area of rhombus = (1/2) × d1 × d2
= (1/2) × 10 × 24
= 120 sq units.
Q. Find the coordinates of the midpoint of the diagonal joining (2, 8) and (10, -4).
A) (6, 2)
B) (5, 2)
C) (4, 3)
D) (6, 4)
Answer: A
Explanation: Midpoint = ((2 + 10)/2 , (8 + (-4))/2)
= (12/2 , 4/2)
= (6 , 2).
Q. If the vertices of a triangle are (0,0), (4,0), and (0,3), then the triangle is:
A) Equilateral
B) Right-angled
C) Isosceles
D) Obtuse-angled
Answer: B
Explanation: The sides along x-axis and y-axis are perpendicular, so the triangle is right-angled.
Q. Find the coordinates of the point which divides the line joining (1, 1) and (7, 13) in the ratio 2:1 internally.
A) (5, 9)
B) (4, 8)
C) (3, 7)
D) (6, 10)
Answer: A
Explanation: Using section formula:
x = (2(7) + 1(1))/3 = 15/3 = 5
y = (2(13) + 1(1))/3 = 27/3 = 9.
Understanding Coordinate Geometry Through Real Graph Positions
Coordinate Geometry mainly focuses on locating points on a graph and understanding how mathematical formulas help calculate distances and positions accurately.
Every point on a graph is represented using an ordered pair:
(x, y)
where:
x represents horizontal position
y represents vertical position
For example:
(3, 2)
(-4, 5)
(0, -6)
These coordinates help students locate points on the Cartesian plane and calculate distances between them mathematically.
This chapter also explains how formulas are used to:
find midpoint of a line segment,
divide lines internally,
and measure distances between points directly on a graph.
Coordinate Geometry becomes much easier when students start visualizing points instead of memorizing formulas only.
Most Important Formulas in Coordinate Geometry
Distance Formula
Distance = √[(x2 − x1)² + (y2 − y1)²]
This formula is used to calculate the distance between two points on the coordinate plane.
Students should simplify calculations carefully because sign mistakes are common while squaring numbers.
Midpoint Formula
[(x1 + x2)/2 , (y1 + y2)/2]
This formula helps students find the exact midpoint between two coordinates.
Midpoint-based objective questions are commonly asked in CBSE exams.
Section Formula
(x, y) = [(mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)]
This formula is used when a point divides a line segment internally in a given ratio.
Students should substitute values carefully because coordinate confusion is very common in section formula questions.
Important Instructions Before Solving Coordinate Geometry MCQs
- Read coordinates carefully before starting calculations because swapping x-values and y-values can change the final answer completely.
- Use formulas step-by-step instead of solving mentally because graph-based calculations require accuracy.
- Check positive and negative signs carefully while substituting values into formulas.
- Keep coordinate values properly organized during calculations to avoid simplification mistakes.
- Revise distance, midpoint, and section formulas regularly because direct formula-based MCQs are common in board exams.
- Visualize graph positions mentally whenever possible because it improves conceptual understanding significantly.
- Practice competency-based and case-study objective questions regularly because the latest CBSE pattern focuses heavily on conceptual application.
- Avoid rushing calculations because most mistakes happen due to improper substitution and sign handling.
Errors Students Commonly Make in Coordinate Geometry
Many students lose marks in Coordinate Geometry MCQs because of avoidable calculation and coordinate substitution mistakes.
Some common errors include:
- Incorrect formula substitution
- Swapping x and y coordinates
- Sign mistakes during calculations
- Wrong midpoint simplification
- Distance formula errors
- Coordinate plotting confusion
- Calculation mistakes involving squares and roots
Students should solve formula-based questions carefully instead of depending completely on shortcuts.
Visual Understanding in Coordinate Geometry
One of the most important skills in this chapter is understanding the position of points visually on a graph.
Students can improve graph understanding by:
- Observing coordinate signs carefully
- Identifying horizontal and vertical movement
- Comparing point positions mentally
- Practicing coordinate plotting regularly
- Understanding quadrants properly
Once students become comfortable with graph visualization, coordinate-based questions become much easier to solve.
Fast Revision Points for Coordinate Geometry
Students should revise these important points regularly before exams:
- x-coordinate shows horizontal movement
- y-coordinate shows vertical movement
- Distance formula measures length between two points
- Midpoint formula gives center point
- Section formula divides a line internally
- Positive and negative signs are important
- Coordinate substitution requires accuracy
- Graph understanding improves solving speed
Short revision sessions help improve retention and board exam confidence significantly.
Final Thoughts
Practicing Coordinate Geometry MCQs with Answers is one of the best ways to improve graph understanding, formula application, and coordinate reasoning skills for Class 10 Maths. This chapter is highly practical because it helps students connect geometry with graphical representation and mathematical calculations together. Students preparing for CBSE board exams should focus on conceptual understanding, careful formula substitution, and regular objective practice instead of memorizing steps blindly. Consistent practice improves calculation accuracy, graph visualization skills, confidence, and overall board exam performance naturally.