CBSE Class 10 Mathematics Chapter 7 Coordinate Geometry Worksheet with Answers

Before attempting the worksheet, revisit these fundamental formulas from NCERT Class 10 Mathematics Chapter 7. The distance formula calculates the length between two points A(x₁, y₁) and B(x₂, y₂) as √[(x₂ − x₁)² + (y₂ − y₁)²]. The section formula divides a line segment internally in ratio m:n, giving coordinates ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n)). For external division, the denominator becomes (m − n). The area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) is ½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. Remember that if three points are collinear, their area equals zero. These three formulas are the backbone of every coordinate geometry problem in CBSE Class 10 board papers and appear in both direct computation and application-based questions. Mark distribution typically includes 2-3 questions: one 2-marker, one 3-marker, and occasionally one integrated 4-5 mark problem combining multiple concepts.

This section contains six multiple-choice questions testing conceptual understanding and quick calculation skills. Each MCQ has been designed to reflect the style of CBSE Class 10 board papers from recent years, where one-mark questions demand precision and speed. Students should aim to complete this section in 10-12 minutes. Common traps include sign errors in the distance formula, confusion between internal and external section formula, and incorrect application of the determinant method for area calculation. Read each option carefully before marking your answer. In the 2024 CBSE board exam, approximately 4-5 MCQs appeared from Coordinate Geometry in the objective section, making this practice crucial. Remember that negative marking is not applied in board exams, but accuracy builds confidence. Pay special attention to questions involving the midpoint formula, which is a special case of section formula with ratio 1:1, and questions that ask for the type of triangle or quadrilateral based on distance calculations between vertices. These integrated questions test multiple concepts simultaneously and are frequently asked.

Five fill-in-the-blank questions are provided here to test recall of formulas, properties, and direct application. Unlike MCQs, these require you to produce the answer rather than recognize it, making them slightly more challenging. CBSE Class 10 Mathematics board papers often include 2-3 such questions in the first section. Students should write answers with correct units where applicable and maintain precision to two decimal places unless the answer is exact. Common topics include finding one coordinate when distance is given, determining the ratio in which a point divides a line segment, or completing statements about collinearity and area properties. Time allocation: 8-10 minutes for this entire section. When the question involves the section formula, clearly identify whether the division is internal or external by reading the problem statement carefully. The phrase 'divides internally' means both segments lie on the same side, while 'divides externally' means the point lies outside the segment. In problems involving area, remember the absolute value notation—areas are always positive. Practice writing numerical answers neatly; unclear handwriting in board exams can cost marks even when the method is correct.

This section contains a match-the-following table with five pairs and four true/false statements, totaling nine marks. Match-the-following questions test your ability to connect concepts, formulas, and their applications quickly. Each item in Column A must be paired with exactly one item in Column B. CBSE board papers in 2023 and 2024 included such questions to assess conceptual clarity without lengthy calculations. For the true/false statements, write 'True' or 'False' clearly; do not use T/F abbreviations unless specifically instructed. These questions often involve properties like 'the diagonals of a rectangle are equal in length' or 'three points with area zero are collinear', which are direct applications of coordinate geometry concepts. Suggested time: 12-15 minutes. A good strategy is to first match or evaluate the items you are most confident about, then return to the trickier ones. In true/false questions, look for absolute terms like 'always', 'never', or 'must'—they often indicate exceptions you should consider. Cross-verify your matches by ensuring no item in Column B is left unpaired and that each pairing makes logical sense within NCERT Class 10 Mathematics Chapter 7 content.

Five short-answer questions are included in this section, each carrying 2 marks for a total of 10 marks. According to CBSE marking schemes from recent years, 2-mark questions require one key formula application and one or two computation steps. Full marks are awarded only when the method is correct and the final answer is accurate; partial credit of 1 mark may be given if the setup is right but a calculation error occurs. Write each step clearly and do not skip intermediate algebra. For instance, when using the distance formula, show the substitution, the squaring, the sum, and the square root separately. Questions in this section may ask you to find an unknown coordinate, verify if points form a specific type of triangle, or calculate the ratio of division. Suggested time: 20 minutes (4 minutes per question). Maintain neat handwriting and box your final answer to make it easy for the examiner to spot. When asked to 'show' or 'verify', write a concluding sentence such as 'Hence, the points form an isosceles triangle' to indicate completion. Students often lose a mark by omitting this final statement. NCERT Class 10 Mathematics solutions books emphasize this step-by-step presentation, which is equally important in board exams.

Three long-answer questions are presented here, carrying 3, 4, and 5 marks respectively for a total of 12 marks. These problems integrate multiple concepts from NCERT Class 10 Mathematics Chapter 7 and often require algebraic manipulation, forming and solving equations, or proving geometric properties using coordinates. HOTS (Higher Order Thinking Skills) questions test application and analysis, not just recall. For example, you may need to prove that a quadrilateral is a parallelogram by showing opposite sides are equal using the distance formula, or find the value of a parameter so that three points are collinear by setting their area to zero. Suggested time: 30-35 minutes (10-12 minutes per question). Write your solution in a logical sequence: given data, formula used, substitution, algebraic steps, and final answer with units. Marks are distributed for method (60-70 percent) and accuracy (30-40 percent), so even if your final answer is incorrect, clear working can fetch most marks. These questions mirror the style of 4-5 mark problems in the 2024 CBSE board paper and are excellent practice for building problem-solving confidence. CBSETUTOR.ai offers 24×7 AI-powered doubt solving where students can upload a photo of such HOTS questions and get step-by-step hints, making self-study far more effective at just ₹999/month across all subjects for Classes 6-12, with a 3-day free trial.

CBSE introduced competency-based case-study questions in 2021, and they now carry 4 marks in every Class 10 Mathematics board paper. The case study presents a real-life scenario or a diagram followed by 3-4 sub-questions (typically three 1-mark MCQs and one 2-mark descriptive). For Coordinate Geometry, scenarios may involve city planning (plotting parks or bus stops on a grid), navigation (ships at sea), architecture (vertices of buildings), or sports fields marked on coordinate planes. Read the case paragraph carefully and extract given coordinates, ratios, or other numerical data. Annotate the diagram if provided. Each sub-question is independent, so even if you are unsure about part (i), attempt parts (ii) and (iii). Time allocation: 10-12 minutes. The 2024 board paper included a case study about a rectangular park with fountains at specific coordinates, asking students to find distances and verify properties. These questions test application, interpretation, and multi-step reasoning—all higher-order skills. Practicing such integrated problems boosts confidence and ensures you do not lose these 4 valuable marks on exam day. NCERT Class 10 Mathematics textbooks now include similar exercises in the miscellaneous section at the chapter end.

Complete solutions for all six multiple-choice questions are provided below with brief explanations. Each answer shows the formula applied, substitution of values, and the final result. Cross-check your responses and note any mistakes for revision. If you chose an incorrect option, revisit the relevant NCERT Class 10 Mathematics Chapter 7 section to strengthen your understanding. Correct answers build speed and accuracy—aim for 5/6 or 6/6 in this section during timed practice. These explanations also serve as quick reference notes before your board exam. If a particular type of question repeatedly causes errors, mark it and practice similar problems from your NCERT textbook or Class 10 Mathematics solutions guides. Understanding why an answer is correct is more important than memorizing it, especially for application-based MCQs where numbers may change but the method remains the same. Use the explanations to self-assess and identify weak areas early in your revision cycle.

This section provides step-by-step solutions for all remaining questions: fill-in-the-blanks, match-the-following, true/false, short answers, long answers, HOTS problems, and the case study. Each answer includes the relevant formula, substitution, working, and final result with units where applicable. For short-answer questions (Section D), marking schemes allocate 1 mark for correct method and 1 mark for correct answer; partial credit is given if only setup is correct. Long-answer solutions (Section E) show every algebraic step to help you understand how to present your work in board exams. The case-study answer key breaks down each sub-question and highlights how to interpret the scenario. Use this comprehensive key not only to check your answers but also to learn the standard format expected by CBSE examiners. If your method differs from the given solution but arrives at the same answer, verify whether all steps are mathematically valid. When preparing for the board exam, practice writing these solutions within the time limits suggested for each section to build speed and confidence. Self-assessment using a detailed answer key is one of the most effective revision strategies, as per educational research and CBSE Class 10 Mathematics toppers.

To extract maximum benefit, print this worksheet and attempt it under timed, exam-like conditions—90 minutes without breaks. Keep your NCERT Class 10 Mathematics textbook, a calculator (if allowed), and graph paper nearby for rough work. Do not refer to solutions until you have attempted every question. After completing the worksheet, spend another 30 minutes reviewing the answer key, marking each question as correct, partially correct, or incorrect. Identify patterns: are you making sign errors in the distance formula? Confusing internal and external section formula? Forgetting the absolute value in area calculations? Create a one-page error log noting these mistakes and revise the relevant theory from NCERT Chapter 7. Reattempt incorrect questions after a day or two to check retention. Use this worksheet as a diagnostic tool three to four weeks before your board exam. For daily doubt clearing and instant photo-based solutions, students across India are turning to CBSETUOR.ai, which offers 24×7 AI tutor support for all chapters in Classes 6-12 at a single price of ₹999/month with a 3-day free trial—perfect for last-minute revision and practice. Regular worksheet practice combined with intelligent doubt resolution builds the confidence needed to score 95+ in CBSE Class 10 Mathematics board exams.