NCERT Solutions for Class 10 Maths Chapter 7: Coordinate Geometry
Coordinate Geometry is that fascinating branch of mathematics where algebra and geometry meet on a grid. Chapter 7 of Class 10 NCERT Maths takes students into the world of the Cartesian plane, where every point has an address and every distance can be calculated using a formula. For students who often find pure geometry tricky because of its reliance on diagrams and intuition, Coordinate Geometry offers a refreshing algebraic approach — you simply plug values into formulas and get answers.
This chapter introduces three fundamental tools: the Distance Formula, the Section Formula, and the formula for finding the Area of a Triangle using coordinates. These are not isolated concepts — they connect directly to real-world applications like GPS systems, map navigation, and architecture. CBSE board exams consistently include questions from this chapter, and the good news is that with enough practice, it is one of the most scoring chapters in the entire Class 10 Maths syllabus. Myclass24 offers completely solved NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry, with each answer broken down clearly so students can verify their work and understand the method. For other chapters of NCERT Solutions for Class 10 Maths, check NCERT Solutions for Class 10 and NCERT Solutions.
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Chapter 7 Coordinate Geometry – Formulas, Facts & Exercise Details
Chapter 7 is built around three core formulas that students need to memorise, understand, and apply confidently. Unlike some chapters where you can get by with partial understanding, Coordinate Geometry is very formula-driven — and every formula has a specific use case that the NCERT exercises test systematically.
Core Formulas at a Glance
| Formula | Expression | Used For |
|---|---|---|
| Distance Formula | d = √[(x₂−x₁)² + (y₂−y₁)²] | Finding distance between two points |
| Section Formula (Internal) | P = [(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)] | Point dividing a segment internally in ratio m:n |
| Midpoint Formula | M = [(x₁+x₂)/2, (y₁+y₂)/2] | Midpoint of a line segment (special case of section formula) |
| Area of Triangle | ½ |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| | Area using vertex coordinates |
Exercise-wise Breakdown of Chapter 7
| Exercise | Main Topic | No. of Questions | Key Skills Tested |
|---|---|---|---|
| Exercise 7.1 | Distance Formula | 10 | Finding distances, checking collinearity, type of triangle/quadrilateral |
| Exercise 7.2 | Section Formula & Midpoint | 10 | Finding coordinates of division points, trisection, centroid |
| Exercise 7.3 | Area of Triangle using Coordinates | 5 | Area calculation, condition for collinear points |
| Exercise 7.4 (Optional) | Mixed application problems | 8 | Advanced coordinate problems |
Chapter-Specific Facts Students Must Know
| Fact | Details |
|---|---|
| Collinear Points | Three points are collinear if the area of the triangle formed by them is zero |
| Origin Distance | Distance of any point (x, y) from origin = √(x² + y²) |
| Centroid Formula | G = [(x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3] — derived from Section Formula |
| External Division | Section Formula also works for external division with a negative ratio sign |
| Real-Life Use | GPS, Google Maps, and city planning all rely on coordinate geometry principles |
Types of Questions Asked in CBSE Board Exams from Chapter 7
- 1-mark questions: Apply the distance or midpoint formula to find a missing coordinate.
- 2-mark questions: Show that given points form a particular type of triangle or quadrilateral.
- 3-mark questions: Use the section formula to find a point dividing a line segment in a given ratio.
- 4/5-mark questions: Prove that given vertices form a specific shape (square, rhombus, parallelogram) using multiple formulas.
An important tip — when using the area formula, always take the absolute value of the result. The formula can give a negative number if the vertices are listed in clockwise order, but area is always positive. Myclass24's NCERT Solutions for Class 10 Maths Chapter 7 clearly show this step in every relevant question, so students do not lose marks on presentation.
NCERT Solutions for Class 10 Maths Chapter 7: Coordinate Geometry
Coordinate Geometry is the branch of mathematics that combines algebra and geometry through a coordinate system. It helps represent points on a plane using ordered pairs of numbers. In Class 10, students mainly learn to find the distance between two points and understand how coordinates are used to locate positions accurately. This chapter is important because it provides a foundation for graphing, geometric proofs, and advanced mathematical concepts. Coordinate Geometry is widely used in engineering, navigation, architecture, and computer graphics, making it one of the most practical topics in mathematics.
The distance formula is used to find the distance between two points on a coordinate plane. It is derived using the Pythagoras Theorem and helps calculate the length of a line segment joining two points. Students use this formula extensively to solve geometric problems involving coordinates. Understanding the distance formula is essential because it forms the basis for many applications in higher mathematics. Examination questions often require students to calculate distances accurately and use them to determine geometric relationships between points.
The distance formula is derived from the Pythagoras Theorem. When two points are plotted on a coordinate plane, a right-angled triangle can be formed using horizontal and vertical distances. Applying the Pythagoras Theorem to this triangle gives the formula for calculating the distance between the points. Understanding the derivation helps students remember the formula more effectively and apply it confidently. This concept also demonstrates how different mathematical topics are interconnected. Questions related to derivation and application frequently appear in school and board examinations.
An ordered pair consists of two numbers written in a specific order to represent the location of a point on a coordinate plane. The first number indicates the horizontal position, while the second number indicates the vertical position. Ordered pairs are important because changing the order changes the location of the point. Students learn how to plot and identify points using ordered pairs. Mastering this concept is necessary for understanding graphs, distances, and geometric relationships. It serves as the foundation of the entire chapter.
Coordinates are used in navigation systems, digital maps, architecture, engineering, and computer graphics. They help determine exact locations and directions. Modern technologies such as GPS rely heavily on coordinate systems to provide accurate positioning. By learning Coordinate Geometry, students understand how mathematics is applied in practical situations. These real-world applications make the chapter more meaningful and demonstrate the importance of coordinates beyond classroom learning. Understanding such applications also increases interest in mathematics and its everyday uses.
Students often make mistakes while plotting points, reading coordinates incorrectly, or substituting values into the distance formula. Another common error is confusing the x-coordinate with the y-coordinate. Calculation mistakes during simplification can also lead to incorrect answers. To avoid these errors, students should label points carefully and verify calculations step by step. Practicing graphs regularly improves accuracy and confidence. Developing a systematic approach helps students solve coordinate geometry problems more effectively during examinations.
Coordinate Geometry acts as a bridge between algebra and geometry. Many advanced topics, including straight lines, circles, conic sections, and vectors, depend on coordinate concepts. A strong understanding of this chapter makes future mathematical studies easier. It also develops logical thinking, visualization skills, and analytical reasoning. Since Coordinate Geometry has applications in science, technology, and engineering, mastering its basics provides long-term academic benefits. Students who understand coordinate concepts thoroughly often find higher-level mathematics more accessible and enjoyable.