Coordinate Geometry — Class 10 MCQs with Answers
Class 10 CBSE Mathematics · Chapter 7
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 10 CBSE Mathematics questions from Chapter 7, "Coordinate Geometry". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE Board exams and the JEE & NEET foundation years apart.
To score well in "Coordinate Geometry", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Coordinate Geometry, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 10 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Coordinate Geometry (Class 10 Mathematics)
Placing a figure on the coordinate plane turns geometric questions into arithmetic. This chapter finds the distance between two points, the point dividing a segment in a given ratio, and the area of a triangle from its vertices alone.
- Distance formula
- The straight-line distance between two points, obtained by applying Pythagoras to the horizontal and vertical gaps.
- Distance from the origin
- A special case of the distance formula, √(x² + y²), used constantly in shorter problems.
- Section formula (internal)
- The coordinates of the point dividing the segment joining two points internally in the ratio m : n.
- Midpoint formula
- The section formula with ratio 1 : 1 — simply the averages of the two endpoints' coordinates.
Coordinate Geometry — important questions & MCQs with answers (Class 10 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
Distance between (0,0) and (3,4) is:
A.4B.7C.5✓ CorrectD.3Answer: C. 5
Explanation: Distance formula √[(x₂−x₁)²+(y₂−y₁)²]: √[(3−0)²+(4−0)²] = √(9+16) = √25 = 5 units.
- Q2Easy
Midpoint of (2,3) and (4,7) is:
A.(6,10)B.(2,5)C.(3,4)D.(3,5)✓ CorrectAnswer: D. (3,5)
Explanation: Midpoint formula ((x₁+x₂)/2, (y₁+y₂)/2): ((2+4)/2, (3+7)/2) = (3, 5).
- Q3Easy
The distance between points (x₁, y₁) and (x₂, y₂) is:
A.(x₂ − x₁)² + (y₂ − y₁)²B.√[(x₂ − x₁)² + (y₂ − y₁)²]✓ CorrectC.|x₂ − x₁| + |y₂ − y₁|D.x₂y₂ − x₁y₁Answer: B. √[(x₂ − x₁)² + (y₂ − y₁)²]
Explanation: Pythagoras theorem on the right triangle with legs (x₂−x₁) and (y₂−y₁) gives distance = √[(x₂−x₁)²+(y₂−y₁)²]; dropping the √ leaves only the squared distance.
- Q4Easy
The coordinates of the point dividing the line segment from (x₁, y₁) to (x₂, y₂) internally in ratio m : n are:
A.((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n))✓ CorrectB.((mx₁ + nx₂)/(m + n), (my₁ + ny₂)/(m + n))C.(mx₂ − nx₁, my₂ − ny₁)D.((x₁ + x₂)/2, (y₁ + y₂)/2)Answer: A. ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n))
Explanation: Section formula for a point dividing AB in ratio m:n internally: ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)); swapping m and n gives a different point.
- Q5Easy
Area of triangle with vertices (x₁, y₁), (x₂, y₂), (x₃, y₃) is:
A.(x₁ + x₂ + x₃)(y₁ + y₂ + y₃)B.(1/2)|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|✓ CorrectC.|x₁y₁ + x₂y₂ + x₃y₃|D.Half the perimeterAnswer: B. (1/2)|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|
Explanation: Area from coordinates: ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)|; the ½ and alternating differences distinguish it from simply multiplying coordinate sums.
- Q6Easy
The distance between the points (0, 0) and (6, 8) is:
A.10✓ CorrectB.14C.2D.48Answer: A. 10
Explanation: The distance is √(6² + 8²) = √100 = 10.
- Q7Medium
Area of triangle with vertices (1,1),(2,2),(3,3):
A.1B.0✓ CorrectC.2D.3Answer: B. 0
Explanation: Area = ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)| = ½|1(2−3)+2(3−1)+3(1−2)| = ½|−1+4−3| = 0, so the points are collinear.
- Q8Medium
Point dividing (2,3) and (8,9) in ratio 1:2 internally is:
A.(6,7)B.(5,6)C.(4,5)✓ CorrectD.(3,4)Answer: C. (4,5)
Explanation: Section formula for ratio m:n = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)): ((1·8+2·2)/3, (1·9+2·3)/3) = (4, 5).
- Q9Medium
If the distance between (a, 0) and (0, 4) is 5, then a equals:
A.±3✓ CorrectB.3C.−3D.±5Answer: A. ±3
Explanation: Distance formula: √(a² + 4²) = 5 ⇒ a² + 16 = 25 ⇒ a² = 9 ⇒ a = ±3. Squaring loses the sign, so both roots are valid — picking only +3 misses one answer.
- Q10Medium
P divides segment AB in ratio 3:2 (internally) where A(2, −1), B(7, 9). P is:
A.(3, 5)B.(4, 3)C.(5, 5)✓ CorrectD.(6, 5)Answer: C. (5, 5)
Explanation: Section formula with ratio 3:2: x = (3·7 + 2·2)/5 = 5, y = (3·9 + 2·(−1))/5 = 5, giving (5, 5).
- Q11Medium
Area of triangle with vertices (1, 2), (4, −3), (6, 5) is:
A.17✓ CorrectB.11C.22D.8Answer: A. 17
Explanation: Area = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| = ½|1(−3−5) + 4(5−2) + 6(2−(−3))| = ½|34| = 17.
- Q12Hard
If (a,0),(0,b) and (1,1) are collinear, then 1/a + 1/b =
A.0B.−1C.1✓ CorrectD.a+bAnswer: C. 1
Explanation: Line through (a,0) and (0,b) has intercept form x/a + y/b = 1; substituting the collinear point (1,1) gives 1/a + 1/b = 1.
- Q13Hard
Centroid of triangle (0,0),(6,0),(0,6) is:
A.(2,2)✓ CorrectB.(3,3)C.(2,3)D.(3,2)Answer: A. (2,2)
Explanation: Centroid formula averages all three vertices: ((0+6+0)/3, (0+0+6)/3) = (2, 2). A common slip is averaging only two vertices or forgetting to divide by 3.
- Q14Hard
The point on y-axis equidistant from (−5, −2) and (3, 2) is:
A.(0, −2)✓ CorrectB.(0, 2)C.(0, 0)D.(0, 3)Answer: A. (0, −2)
Explanation: Let P(0, y). 25 + (y + 2)² = 9 + (y − 2)² ⇒ 25 + y² + 4y + 4 = 9 + y² − 4y + 4 ⇒ 29 + 4y = 13 − 4y ⇒ 8y = −16 ⇒ y = −2.
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Start this chapter free →Coordinate Geometry — FAQs
What are the key concepts in Class 10 Mathematics Coordinate Geometry?+
Placing a figure on the coordinate plane turns geometric questions into arithmetic. This chapter finds the distance between two points, the point dividing a segment in a given ratio, and the area of a triangle from its vertices alone. Key ideas include Distance formula, Distance from the origin, Section formula (internal), Midpoint formula.
What does Class 10 Mathematics Chapter 7 (Coordinate Geometry) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Coordinate Geometry": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "Coordinate Geometry" questions free to practise?+
Yes. Sign in with Google to practise "Coordinate Geometry" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Coordinate Geometry" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Coordinate Geometry" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Coordinate Geometry" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Coordinate Geometry (Class 10 Mathematics)?+
The questions that matter most test Distance formula, Distance from the origin, Section formula (internal), Midpoint formula. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Coordinate Geometry?+
Yes — Class 10 Mathematics Coordinate Geometry has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.