NCERT Solutions Class 10 Maths Chapter 7 guides you through Coordinate Geometry with clear solutions to all 20 questions across 2 exercises. You’ll learn how to apply the distance formula to find lengths between points, use the section formula to locate points dividing line segments in given ratios, and calculate the area of triangles using coordinates. These formulas are essential for solving geometry problems algebraically and appear frequently in board exams.
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All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 10 Maths Chapter 7 Coordinate Geometry – Complete Guide
NCERT Class 10 Chapter 7 – Coordinate Geometry builds upon your foundational knowledge from Class 9 and introduces powerful techniques to solve geometric problems algebraically. You’ll explore three fundamental concepts: the distance formula to calculate the length between any two points, the section formula to find coordinates of points dividing line segments internally or externally, and the area formula to determine the area of triangles formed by three given points.
📊 CBSE Class 10 Maths Chapter 7 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 6 Marks |
| Unit Name | Coordinate Geometry |
| Difficulty Level | Medium |
| Importance | High |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 2-3 questions |
This chapter carries significant weightage of 6 marks in the CBSE board examination, making it crucial for your overall score. You’ll encounter a mix of question types including 2-mark MCQs, 3-mark short answer questions asking you to apply formulas directly, and 5-mark long answer questions requiring multi-step problem solving. The beauty of coordinate geometry lies in its practical applications—from navigation systems and GPS technology to computer graphics and architecture.
You’ll discover how to prove geometric properties like collinearity of points, verify if a quadrilateral is a parallelogram or rhombus, and find coordinates of the fourth vertex of a parallelogram. The chapter seamlessly connects algebraic methods with geometric visualization, strengthening your analytical thinking. Special attention should be given to the section formula as it frequently appears in board exams in various forms.
Quick Facts – Class 10 Chapter 7
| 📖 Chapter Number | Chapter 7 |
| 📚 Chapter Name | Coordinate Geometry |
| ✏️ Total Exercises | 2 Exercises |
| ❓ Total Questions | 20 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Mastering this chapter will not only help you score well in your Class 10 boards but also prepare you for advanced topics in Class 11 like straight lines and conic sections. With consistent practice of NCERT solutions and previous year questions, you’ll develop the confidence to tackle any coordinate geometry problem efficiently and accurately.
NCERT Solutions Class 10 Maths Chapter 7 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| Exercise 7.1 | Complete step-by-step solutions for 10 questions | 📥 Download PDF |
| Exercise 7.2 | Complete step-by-step solutions for 10 questions | 📥 Download PDF |
Coordinate Geometry – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Distance Formula \(d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}\) | Calculates the distance between two points (x₁, y₁) and (x₂, y₂) in the coordinate plane. Note: The order of subtraction doesn’t matter because of the squaring. Make sure to square the differences before adding. | Finding the length of a line segment, checking if points are equidistant, determining the type of triangle/quadrilateral. |
| Section Formula \( (x, y) = \left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right) \) | Finds the coordinates of a point that divides a line segment joining (x₁, y₁) and (x₂, y₂) in the ratio m:n internally. Note: m and n are the parts of the ratio, not the coordinates themselves. Remember the order of x1, x2 and y1, y2. | When a point divides a line segment into a given ratio, especially in problems involving collinearity or finding unknown coordinates. |
| Midpoint Formula \( (x, y) = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \) | Finds the coordinates of the midpoint of a line segment joining (x₁, y₁) and (x₂, y₂). Note: A special case of the section formula where m:n = 1:1. Simply average the x-coordinates and the y-coordinates. | When you need to find the center point of a line segment, especially in problems involving parallelograms or circles. |
| Centroid Formula \( (x, y) = \left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) \) | Finds the coordinates of the centroid (intersection of medians) of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃). Note: The centroid divides each median in the ratio 2:1. Average of all x-coordinates and y-coordinates. | Finding the balancing point of a triangle, or solving problems involving medians. |
| Area of a Triangle (Coordinate Form) \(\text{Area} = \frac{1}{2} |x_1(y_2 – y_3) + x_2(y_3 – y_1) + x_3(y_1 – y_2)|\) | Calculates the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃). Note: The absolute value ensures the area is always positive. If the area is 0, the points are collinear. Remember the cyclic order 123, 231, 312. | When you know the coordinates of the vertices of a triangle and need to find its area. Important for proving collinearity. |
| Condition for Collinearity \(x_1(y_2 – y_3) + x_2(y_3 – y_1) + x_3(y_1 – y_2) = 0\) | Checks if three points (x₁, y₁), (x₂, y₂), and (x₃, y₃) are collinear (lie on the same line). Note: This is derived from the area of a triangle formula. If the area is zero, the points are collinear. | Proving that three points lie on the same line. Useful when a question asks to show points are collinear. |
| Distance from x-axis \( |y| \) | The distance of a point (x, y) from the x-axis Note: The distance is always positive. It’s simply the absolute value of the y-coordinate. | Find the distance of a point from the x-axis. Useful in some locus problems. |
| Distance from y-axis \( |x| \) | The distance of a point (x, y) from the y-axis Note: The distance is always positive. It’s simply the absolute value of the x-coordinate. | Find the distance of a point from the y-axis. Useful in some locus problems. |
| Section Formula (External Division) \( (x, y) = \left(\frac{mx_2 – nx_1}{m-n}, \frac{my_2 – ny_1}{m-n}\right) \) | Finds the coordinates of a point that divides a line segment joining (x₁, y₁) and (x₂, y₂) in the ratio m:n externally. Note: Notice the minus signs. m and n are the parts of the ratio. Make sure m ≠ n. | When a point divides a line segment into a given ratio externally. Rare but important for some advanced problems. |
Frequently Asked Questions – NCERT Class 10 Maths Chapter 7
📚 Related Study Materials – Class 10 Maths Resources
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| NCERT Class 10 English Solutions | View Solutions |