Important Questions: CBSE Class 10 Mathematics Chapter 7 Coordinate Geometry

Chapter 7 Coordinate Geometry appears in Unit III (Geometry) of the CBSE Class 10 Mathematics syllabus. The chapter introduces three core formulas: the distance formula to find the length between two points, the section formula to locate a point dividing a line segment in a given ratio, and the area formula for a triangle when vertices are given as coordinates. In the 2025 Board exam pattern, this chapter typically contributes 6 marks. These marks are distributed as one 1-mark MCQ or VSA, one or two 2-mark questions, one 3-mark question, and occasionally a 5-mark integrated or case-based question that combines coordinate geometry with other chapters like triangles or circles. The NCERT textbook covers all three formulas with derivations and examples, so every question in the Board paper will use NCERT terminology and notation. Students must be comfortable with substituting coordinates into formulas, simplifying square roots, handling plus-minus signs in section formula, and applying the modulus operation for area. Mastery of algebraic manipulation is as important as knowing the formulas themselves.

One-mark questions test instant recall and single-step calculation. They often appear as multiple-choice questions in Section A of the Board paper. Expect questions that ask for distance between two given points, the midpoint formula (a special case of section formula with ratio 1:1), or identification of a coordinate given certain conditions. The key is speed and accuracy—no working is required, but mental calculation must be flawless. Practice these under timed conditions. Below are four representative 1-mark questions with answers that mirror the 2023-25 CBSE pattern. Each answer is direct and uses the exact formula from NCERT. Remember that even a single arithmetic slip costs you the full mark, so double-check sign and square-root simplification before marking your final answer on the OMR sheet or in the answer booklet during the Board exam.

Two-mark questions require you to write formula, substitute values, simplify, and state the answer. They test understanding of section formula or verification-type problems such as checking collinearity of three points or verifying that four points form a specific quadrilateral. Marks are awarded for correct formula (½ mark), substitution (½ mark), working (½ mark), and final answer (½ mark). Always write the formula first, even if you know the answer mentally, because that secures method marks. Below are four 2-mark questions taken from CBSE sample papers and previous years, with complete step-by-step model answers. Practice writing these solutions neatly within the two-minute per mark guideline, which means four minutes per question during the Board exam. Show every arithmetic step to maximise partial credit if you make a small error late in the calculation process.

Three-mark questions are the backbone of this chapter in the Board exam. They typically involve application of the area formula for a triangle given three vertices, or a multi-step problem such as finding an unknown coordinate when area or distance is given, or proving that a set of points forms a particular shape. The area formula is Area = ½ |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|. Notice the absolute value; many students lose a mark by forgetting it. Marks are split: formula statement (½ mark), correct substitution (1 mark), simplification (1 mark), final answer (½ mark). Below are four representative 3-mark questions with full model answers. Write every intermediate step clearly. If the question says 'show' or 'prove', conclude with a statement that directly answers the question. Examiners appreciate logical flow and clarity, which can earn you the benefit of doubt if arithmetic is slightly off.

Five-mark questions test your ability to integrate multiple concepts. They may present a real-world scenario—positions of villages on a map, layout of a park, or a navigation problem—and ask you to find distances, areas, and ratios in sequence. Since 2021, CBSE has included case-based or integrated questions in Section D. A typical case study gives a paragraph description, a diagram or coordinate set, and then asks four to five sub-questions of 1 mark each, totalling 4 or 5 marks. Alternatively, a single 5-mark structured question might ask you to find an unknown coordinate, prove collinearity, compute area, and verify a geometric property all in one go. Below are three 5-mark problems with detailed solutions. Budget roughly 10-12 minutes per 5-mark question in the exam. Read the entire question first, underline what is given and what is asked, then tackle sub-parts in order. Even if you cannot solve part (c), attempt parts (a) and (b) to secure partial marks.

CBSE question-setters follow NCERT exemplar and sample papers closely. They favour questions that require students to apply formulas in unfamiliar contexts rather than rote recall. For distance formula, expect problems where one or both coordinates are negative, or where distance is given and you must find an unknown coordinate. Section formula questions often embed the ratio in a word problem—'a point P divides AB such that AP is twice PB'—requiring you to express the ratio as 2:1 before substituting. Area problems may give three vertices with algebraic expressions (e.g. vertex at (k, 2k)), forcing you to set up an equation and solve for k. Multi-step problems combine two or more concepts: find midpoint, then use it as a vertex to find area of another triangle. Case studies present real-world scenarios—map coordinates, navigation, land plots—with a diagram and several linked sub-questions. The mark scheme rewards clear formula statements, correct substitutions, logical steps, and a boxed or underlined final answer. Negative marking does not apply in subjective sections, so always attempt every part. If stuck, write the formula and any partial working; examiners award step marks generously when method is visible.

Every year, students lose marks in Coordinate Geometry not because they do not know the formulas, but because of avoidable errors in execution. The most frequent mistake is sign errors when coordinates are negative: forgetting that subtracting a negative becomes addition. In section formula, students often confuse internal and external division; NCERT Class 10 covers only internal division, so unless the question specifies external, use the standard formula. Another pitfall is omitting the absolute value in the area formula, leading to a negative area and loss of ½ mark. Students also mix up x and y coordinates—writing (y₁, x₁) instead of (x₁, y₁)—especially under exam pressure. In multi-step problems, some students calculate an intermediate result (e.g. midpoint) but forget to use it in the next part, or they round off too early and carry forward a wrong value. To avoid these mistakes, develop a checklist habit: write the formula first, label all given values (x₁=?, y₁=?, m=?, n=?), substitute carefully with brackets around negative numbers, simplify one operation at a time, and box your final answer. Practice past-year CBSE papers under timed conditions so that accuracy becomes automatic. If you make a mistake during practice, write it in a separate error log and review it weekly.

Here are three more questions—two at 3 marks and one at 2 marks—to round out your practice set. These mirror the latest CBSE pattern and cover areas not fully addressed in earlier sections, such as finding unknown coordinates when other conditions are given, or proving geometric properties using coordinate methods. Work through these under exam conditions: no calculator, neat presentation, and formula stated first. After solving, compare your method with the model answer to identify any gaps in logic or calculation. Remember that CBSE values clarity and stepwise reasoning, so even if you reach the correct answer by a shortcut, writing the standard method ensures you receive full marks. These practice questions also illustrate how the same formula can be used in different contexts, building your confidence to handle unseen problems in the Board exam. Keep your solutions organised in a dedicated notebook so you can revise them quickly in the final week before the exam, alongside your NCERT textbook examples and CBSETUTOR.ai doubt-clearance sessions.

With 6 marks at stake, you cannot afford to skip or under-prepare Coordinate Geometry. Start revision three weeks before the exam. In Week 1, re-read NCERT theory and derivations; understand why each formula works, not just what it is. Solve all NCERT exercises (7.1, 7.2) without looking at solutions, then cross-check. In Week 2, tackle the 18 questions in this question bank under timed conditions—allocate 1 minute per mark—and self-assess using the model answers. Identify your weak areas: Is it sign errors? Forgetting absolute value? Confusing section formula? Make a one-page formula sheet with all three formulas, key points about internal division, and a checklist of common mistakes. In Week 3, solve five previous-year CBSE papers (2020-24) and mark yourself strictly. For every mistake, write the correct solution in your error log. Two days before the exam, revise your formula sheet and error log, and solve one or two case-based questions from CBSE sample papers. On the eve of the exam, avoid new problems; instead, mentally rehearse the steps for distance, section, and area formulas. During the exam, if you are stuck on a coordinate geometry question, move on and return to it—these problems yield marks when you show working, so even partial attempts are valuable. Platforms like CBSETUOR.ai can clarify last-minute doubts via photo upload, ensuring you walk into the exam hall confident and prepared.

Coordinate Geometry is one of those chapters where a single doubt—'Why is it mx₂+nx₁ and not mx₁+nx₂?'—can cascade into confusion across multiple problems. CBSETUTOR.ai offers a 24×7 AI tutor that answers your questions instantly by photo upload. Snap a picture of any problem from NCERT, sample papers, or this question bank, and the AI provides a step-by-step solution with explanations in simple language. Crucially, the AI does not just give you the answer; it walks you through the logic, highlights where students commonly go wrong, and suggests similar practice problems to reinforce the concept. The platform covers all subjects for CBSE Classes 6-12 at a flat ₹999 per month, with no hidden fees and a 3-day free trial so you can try it risk-free before your Board exam. Parents appreciate the value: instead of spending thousands on multiple subject tuitions, one subscription gives your child unlimited access to doubt solving, video explanations, and curated question banks across Maths, Science, Social Science, and languages. For Coordinate Geometry specifically, you can upload case-study screenshots, tricky area problems, or even your own worked solutions for the AI to review and correct. This immediate feedback loop accelerates learning and builds exam confidence. Many students use CBSETUTOR.ai in the final revision phase to clear lingering doubts without waiting for the next tuition class. Try the 3-day free trial and see how AI-powered personalised learning transforms your preparation for Chapter 7 and beyond.